Ramsey Numbers of Trees Versus Multiple Copies of Books
Abstract Given two graphs G and H, the Ramsey number R(G,H) is the minimum integer N such that any two-coloring of the edges of KN in red or blue yields a red G or a blue H. Let v(G) be the number of vertices of G and χ(G) be the chromatic number of G. Let s(G) denote the chromatic surplus of G, the...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Guo, Xiao-bing [verfasserIn] Hu, Si-nan [verfasserIn] Peng, Yue-jian [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2023 |
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| Schlagwörter: |
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| Anmerkung: |
© The Editorial Office of AMAS & Springer-Verlag GmbH Germany 2024 |
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| Übergeordnetes Werk: |
Enthalten in: Acta mathematicae applicatae sinica - Springer Berlin Heidelberg, 1984, 40(2023), 3 vom: 29. Dez., Seite 600-612 |
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| Übergeordnetes Werk: |
volume:40 ; year:2023 ; number:3 ; day:29 ; month:12 ; pages:600-612 |
| Links: |
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| DOI / URN: |
10.1007/s10255-024-1117-4 |
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| Katalog-ID: |
SPR056126158 |
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| 520 | |a Abstract Given two graphs G and H, the Ramsey number R(G,H) is the minimum integer N such that any two-coloring of the edges of KN in red or blue yields a red G or a blue H. Let v(G) be the number of vertices of G and χ(G) be the chromatic number of G. Let s(G) denote the chromatic surplus of G, the number of vertices in a minimum color class among all proper χ(G)-colorings of G. Burr showed that $$R(G,H) \ge (v(G) - 1)(\chi (H) - 1) + s(H)$$ if G is connected and $$v(G) \ge s(H)$$. A connected graph G is H-good if $$R(G,H) = (v(G) - 1)(\chi (H) - 1) + s(H)$$. Let tH denote the disjoint union of t copies of graph H, and let $$G \vee H$$ denote the join of G and H. Denote a complete graph on n vertices by Kn, and a tree on n vertices by Tn. Denote a book with n pages by Bn, i.e., the join $${K_2} \vee \overline {{K_n}} $$. Erdős, Faudree, Rousseau and Schelp proved that Tn is Bm-good if $$n \ge 3m - 3$$. In this paper, we obtain the exact Ramsey number of Tn versus 2B2- Our result implies that Tn is 2B2-good if n ≥ 5. | ||
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10.1007/s10255-024-1117-4 doi (DE-627)SPR056126158 (SPR)s10255-024-1117-4-e DE-627 ger DE-627 rakwb eng 510 VZ ASIEN DE-1a fid 31.80 bkl Guo, Xiao-bing verfasserin aut Ramsey Numbers of Trees Versus Multiple Copies of Books 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Editorial Office of AMAS & Springer-Verlag GmbH Germany 2024 Abstract Given two graphs G and H, the Ramsey number R(G,H) is the minimum integer N such that any two-coloring of the edges of KN in red or blue yields a red G or a blue H. Let v(G) be the number of vertices of G and χ(G) be the chromatic number of G. Let s(G) denote the chromatic surplus of G, the number of vertices in a minimum color class among all proper χ(G)-colorings of G. Burr showed that $$R(G,H) \ge (v(G) - 1)(\chi (H) - 1) + s(H)$$ if G is connected and $$v(G) \ge s(H)$$. A connected graph G is H-good if $$R(G,H) = (v(G) - 1)(\chi (H) - 1) + s(H)$$. Let tH denote the disjoint union of t copies of graph H, and let $$G \vee H$$ denote the join of G and H. Denote a complete graph on n vertices by Kn, and a tree on n vertices by Tn. Denote a book with n pages by Bn, i.e., the join $${K_2} \vee \overline {{K_n}} $$. Erdős, Faudree, Rousseau and Schelp proved that Tn is Bm-good if $$n \ge 3m - 3$$. In this paper, we obtain the exact Ramsey number of Tn versus 2B2- Our result implies that Tn is 2B2-good if n ≥ 5. ramsey number (dpeaa)DE-He213 ramsey goodness (dpeaa)DE-He213 tree (dpeaa)DE-He213 book (dpeaa)DE-He213 Hu, Si-nan verfasserin aut Peng, Yue-jian verfasserin aut Enthalten in Acta mathematicae applicatae sinica Springer Berlin Heidelberg, 1984 40(2023), 3 vom: 29. Dez., Seite 600-612 (DE-627)345617312 (DE-600)2076073-5 1618-3932 nnns volume:40 year:2023 number:3 day:29 month:12 pages:600-612 https://dx.doi.org/10.1007/s10255-024-1117-4 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER FID-ASIEN SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2036 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2700 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 31.80 VZ AR 40 2023 3 29 12 600-612 |
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10.1007/s10255-024-1117-4 doi (DE-627)SPR056126158 (SPR)s10255-024-1117-4-e DE-627 ger DE-627 rakwb eng 510 VZ ASIEN DE-1a fid 31.80 bkl Guo, Xiao-bing verfasserin aut Ramsey Numbers of Trees Versus Multiple Copies of Books 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Editorial Office of AMAS & Springer-Verlag GmbH Germany 2024 Abstract Given two graphs G and H, the Ramsey number R(G,H) is the minimum integer N such that any two-coloring of the edges of KN in red or blue yields a red G or a blue H. Let v(G) be the number of vertices of G and χ(G) be the chromatic number of G. Let s(G) denote the chromatic surplus of G, the number of vertices in a minimum color class among all proper χ(G)-colorings of G. Burr showed that $$R(G,H) \ge (v(G) - 1)(\chi (H) - 1) + s(H)$$ if G is connected and $$v(G) \ge s(H)$$. A connected graph G is H-good if $$R(G,H) = (v(G) - 1)(\chi (H) - 1) + s(H)$$. Let tH denote the disjoint union of t copies of graph H, and let $$G \vee H$$ denote the join of G and H. Denote a complete graph on n vertices by Kn, and a tree on n vertices by Tn. Denote a book with n pages by Bn, i.e., the join $${K_2} \vee \overline {{K_n}} $$. Erdős, Faudree, Rousseau and Schelp proved that Tn is Bm-good if $$n \ge 3m - 3$$. In this paper, we obtain the exact Ramsey number of Tn versus 2B2- Our result implies that Tn is 2B2-good if n ≥ 5. ramsey number (dpeaa)DE-He213 ramsey goodness (dpeaa)DE-He213 tree (dpeaa)DE-He213 book (dpeaa)DE-He213 Hu, Si-nan verfasserin aut Peng, Yue-jian verfasserin aut Enthalten in Acta mathematicae applicatae sinica Springer Berlin Heidelberg, 1984 40(2023), 3 vom: 29. Dez., Seite 600-612 (DE-627)345617312 (DE-600)2076073-5 1618-3932 nnns volume:40 year:2023 number:3 day:29 month:12 pages:600-612 https://dx.doi.org/10.1007/s10255-024-1117-4 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER FID-ASIEN SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2036 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2700 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 31.80 VZ AR 40 2023 3 29 12 600-612 |
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10.1007/s10255-024-1117-4 doi (DE-627)SPR056126158 (SPR)s10255-024-1117-4-e DE-627 ger DE-627 rakwb eng 510 VZ ASIEN DE-1a fid 31.80 bkl Guo, Xiao-bing verfasserin aut Ramsey Numbers of Trees Versus Multiple Copies of Books 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Editorial Office of AMAS & Springer-Verlag GmbH Germany 2024 Abstract Given two graphs G and H, the Ramsey number R(G,H) is the minimum integer N such that any two-coloring of the edges of KN in red or blue yields a red G or a blue H. Let v(G) be the number of vertices of G and χ(G) be the chromatic number of G. Let s(G) denote the chromatic surplus of G, the number of vertices in a minimum color class among all proper χ(G)-colorings of G. Burr showed that $$R(G,H) \ge (v(G) - 1)(\chi (H) - 1) + s(H)$$ if G is connected and $$v(G) \ge s(H)$$. A connected graph G is H-good if $$R(G,H) = (v(G) - 1)(\chi (H) - 1) + s(H)$$. Let tH denote the disjoint union of t copies of graph H, and let $$G \vee H$$ denote the join of G and H. Denote a complete graph on n vertices by Kn, and a tree on n vertices by Tn. Denote a book with n pages by Bn, i.e., the join $${K_2} \vee \overline {{K_n}} $$. Erdős, Faudree, Rousseau and Schelp proved that Tn is Bm-good if $$n \ge 3m - 3$$. In this paper, we obtain the exact Ramsey number of Tn versus 2B2- Our result implies that Tn is 2B2-good if n ≥ 5. ramsey number (dpeaa)DE-He213 ramsey goodness (dpeaa)DE-He213 tree (dpeaa)DE-He213 book (dpeaa)DE-He213 Hu, Si-nan verfasserin aut Peng, Yue-jian verfasserin aut Enthalten in Acta mathematicae applicatae sinica Springer Berlin Heidelberg, 1984 40(2023), 3 vom: 29. Dez., Seite 600-612 (DE-627)345617312 (DE-600)2076073-5 1618-3932 nnns volume:40 year:2023 number:3 day:29 month:12 pages:600-612 https://dx.doi.org/10.1007/s10255-024-1117-4 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER FID-ASIEN SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2036 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2700 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 31.80 VZ AR 40 2023 3 29 12 600-612 |
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10.1007/s10255-024-1117-4 doi (DE-627)SPR056126158 (SPR)s10255-024-1117-4-e DE-627 ger DE-627 rakwb eng 510 VZ ASIEN DE-1a fid 31.80 bkl Guo, Xiao-bing verfasserin aut Ramsey Numbers of Trees Versus Multiple Copies of Books 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Editorial Office of AMAS & Springer-Verlag GmbH Germany 2024 Abstract Given two graphs G and H, the Ramsey number R(G,H) is the minimum integer N such that any two-coloring of the edges of KN in red or blue yields a red G or a blue H. Let v(G) be the number of vertices of G and χ(G) be the chromatic number of G. Let s(G) denote the chromatic surplus of G, the number of vertices in a minimum color class among all proper χ(G)-colorings of G. Burr showed that $$R(G,H) \ge (v(G) - 1)(\chi (H) - 1) + s(H)$$ if G is connected and $$v(G) \ge s(H)$$. A connected graph G is H-good if $$R(G,H) = (v(G) - 1)(\chi (H) - 1) + s(H)$$. Let tH denote the disjoint union of t copies of graph H, and let $$G \vee H$$ denote the join of G and H. Denote a complete graph on n vertices by Kn, and a tree on n vertices by Tn. Denote a book with n pages by Bn, i.e., the join $${K_2} \vee \overline {{K_n}} $$. Erdős, Faudree, Rousseau and Schelp proved that Tn is Bm-good if $$n \ge 3m - 3$$. In this paper, we obtain the exact Ramsey number of Tn versus 2B2- Our result implies that Tn is 2B2-good if n ≥ 5. ramsey number (dpeaa)DE-He213 ramsey goodness (dpeaa)DE-He213 tree (dpeaa)DE-He213 book (dpeaa)DE-He213 Hu, Si-nan verfasserin aut Peng, Yue-jian verfasserin aut Enthalten in Acta mathematicae applicatae sinica Springer Berlin Heidelberg, 1984 40(2023), 3 vom: 29. Dez., Seite 600-612 (DE-627)345617312 (DE-600)2076073-5 1618-3932 nnns volume:40 year:2023 number:3 day:29 month:12 pages:600-612 https://dx.doi.org/10.1007/s10255-024-1117-4 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER FID-ASIEN SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2036 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2700 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 31.80 VZ AR 40 2023 3 29 12 600-612 |
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10.1007/s10255-024-1117-4 doi (DE-627)SPR056126158 (SPR)s10255-024-1117-4-e DE-627 ger DE-627 rakwb eng 510 VZ ASIEN DE-1a fid 31.80 bkl Guo, Xiao-bing verfasserin aut Ramsey Numbers of Trees Versus Multiple Copies of Books 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Editorial Office of AMAS & Springer-Verlag GmbH Germany 2024 Abstract Given two graphs G and H, the Ramsey number R(G,H) is the minimum integer N such that any two-coloring of the edges of KN in red or blue yields a red G or a blue H. Let v(G) be the number of vertices of G and χ(G) be the chromatic number of G. Let s(G) denote the chromatic surplus of G, the number of vertices in a minimum color class among all proper χ(G)-colorings of G. Burr showed that $$R(G,H) \ge (v(G) - 1)(\chi (H) - 1) + s(H)$$ if G is connected and $$v(G) \ge s(H)$$. A connected graph G is H-good if $$R(G,H) = (v(G) - 1)(\chi (H) - 1) + s(H)$$. Let tH denote the disjoint union of t copies of graph H, and let $$G \vee H$$ denote the join of G and H. Denote a complete graph on n vertices by Kn, and a tree on n vertices by Tn. Denote a book with n pages by Bn, i.e., the join $${K_2} \vee \overline {{K_n}} $$. Erdős, Faudree, Rousseau and Schelp proved that Tn is Bm-good if $$n \ge 3m - 3$$. In this paper, we obtain the exact Ramsey number of Tn versus 2B2- Our result implies that Tn is 2B2-good if n ≥ 5. ramsey number (dpeaa)DE-He213 ramsey goodness (dpeaa)DE-He213 tree (dpeaa)DE-He213 book (dpeaa)DE-He213 Hu, Si-nan verfasserin aut Peng, Yue-jian verfasserin aut Enthalten in Acta mathematicae applicatae sinica Springer Berlin Heidelberg, 1984 40(2023), 3 vom: 29. Dez., Seite 600-612 (DE-627)345617312 (DE-600)2076073-5 1618-3932 nnns volume:40 year:2023 number:3 day:29 month:12 pages:600-612 https://dx.doi.org/10.1007/s10255-024-1117-4 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER FID-ASIEN SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_636 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2036 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2700 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 31.80 VZ AR 40 2023 3 29 12 600-612 |
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Enthalten in Acta mathematicae applicatae sinica 40(2023), 3 vom: 29. Dez., Seite 600-612 volume:40 year:2023 number:3 day:29 month:12 pages:600-612 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">SPR056126158</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20240606064647.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">240606s2023 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10255-024-1117-4</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR056126158</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s10255-024-1117-4-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">ASIEN</subfield><subfield code="q">DE-1a</subfield><subfield code="2">fid</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.80</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Guo, Xiao-bing</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Ramsey Numbers of Trees Versus Multiple Copies of Books</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2023</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Editorial Office of AMAS & Springer-Verlag GmbH Germany 2024</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Given two graphs G and H, the Ramsey number R(G,H) is the minimum integer N such that any two-coloring of the edges of KN in red or blue yields a red G or a blue H. Let v(G) be the number of vertices of G and χ(G) be the chromatic number of G. Let s(G) denote the chromatic surplus of G, the number of vertices in a minimum color class among all proper χ(G)-colorings of G. Burr showed that $$R(G,H) \ge (v(G) - 1)(\chi (H) - 1) + s(H)$$ if G is connected and $$v(G) \ge s(H)$$. A connected graph G is H-good if $$R(G,H) = (v(G) - 1)(\chi (H) - 1) + s(H)$$. Let tH denote the disjoint union of t copies of graph H, and let $$G \vee H$$ denote the join of G and H. Denote a complete graph on n vertices by Kn, and a tree on n vertices by Tn. Denote a book with n pages by Bn, i.e., the join $${K_2} \vee \overline {{K_n}} $$. Erdős, Faudree, Rousseau and Schelp proved that Tn is Bm-good if $$n \ge 3m - 3$$. 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Guo, Xiao-bing |
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510 VZ ASIEN DE-1a fid 31.80 bkl Ramsey Numbers of Trees Versus Multiple Copies of Books ramsey number (dpeaa)DE-He213 ramsey goodness (dpeaa)DE-He213 tree (dpeaa)DE-He213 book (dpeaa)DE-He213 |
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marc |
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2023 |
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Guo, Xiao-bing Hu, Si-nan Peng, Yue-jian |
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Elektronische Aufsätze |
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Guo, Xiao-bing |
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10.1007/s10255-024-1117-4 |
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510 |
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verfasserin |
| title_sort |
ramsey numbers of trees versus multiple copies of books |
| title_auth |
Ramsey Numbers of Trees Versus Multiple Copies of Books |
| abstract |
Abstract Given two graphs G and H, the Ramsey number R(G,H) is the minimum integer N such that any two-coloring of the edges of KN in red or blue yields a red G or a blue H. Let v(G) be the number of vertices of G and χ(G) be the chromatic number of G. Let s(G) denote the chromatic surplus of G, the number of vertices in a minimum color class among all proper χ(G)-colorings of G. Burr showed that $$R(G,H) \ge (v(G) - 1)(\chi (H) - 1) + s(H)$$ if G is connected and $$v(G) \ge s(H)$$. A connected graph G is H-good if $$R(G,H) = (v(G) - 1)(\chi (H) - 1) + s(H)$$. Let tH denote the disjoint union of t copies of graph H, and let $$G \vee H$$ denote the join of G and H. Denote a complete graph on n vertices by Kn, and a tree on n vertices by Tn. Denote a book with n pages by Bn, i.e., the join $${K_2} \vee \overline {{K_n}} $$. Erdős, Faudree, Rousseau and Schelp proved that Tn is Bm-good if $$n \ge 3m - 3$$. In this paper, we obtain the exact Ramsey number of Tn versus 2B2- Our result implies that Tn is 2B2-good if n ≥ 5. © The Editorial Office of AMAS & Springer-Verlag GmbH Germany 2024 |
| abstractGer |
Abstract Given two graphs G and H, the Ramsey number R(G,H) is the minimum integer N such that any two-coloring of the edges of KN in red or blue yields a red G or a blue H. Let v(G) be the number of vertices of G and χ(G) be the chromatic number of G. Let s(G) denote the chromatic surplus of G, the number of vertices in a minimum color class among all proper χ(G)-colorings of G. Burr showed that $$R(G,H) \ge (v(G) - 1)(\chi (H) - 1) + s(H)$$ if G is connected and $$v(G) \ge s(H)$$. A connected graph G is H-good if $$R(G,H) = (v(G) - 1)(\chi (H) - 1) + s(H)$$. Let tH denote the disjoint union of t copies of graph H, and let $$G \vee H$$ denote the join of G and H. Denote a complete graph on n vertices by Kn, and a tree on n vertices by Tn. Denote a book with n pages by Bn, i.e., the join $${K_2} \vee \overline {{K_n}} $$. Erdős, Faudree, Rousseau and Schelp proved that Tn is Bm-good if $$n \ge 3m - 3$$. In this paper, we obtain the exact Ramsey number of Tn versus 2B2- Our result implies that Tn is 2B2-good if n ≥ 5. © The Editorial Office of AMAS & Springer-Verlag GmbH Germany 2024 |
| abstract_unstemmed |
Abstract Given two graphs G and H, the Ramsey number R(G,H) is the minimum integer N such that any two-coloring of the edges of KN in red or blue yields a red G or a blue H. Let v(G) be the number of vertices of G and χ(G) be the chromatic number of G. Let s(G) denote the chromatic surplus of G, the number of vertices in a minimum color class among all proper χ(G)-colorings of G. Burr showed that $$R(G,H) \ge (v(G) - 1)(\chi (H) - 1) + s(H)$$ if G is connected and $$v(G) \ge s(H)$$. A connected graph G is H-good if $$R(G,H) = (v(G) - 1)(\chi (H) - 1) + s(H)$$. Let tH denote the disjoint union of t copies of graph H, and let $$G \vee H$$ denote the join of G and H. Denote a complete graph on n vertices by Kn, and a tree on n vertices by Tn. Denote a book with n pages by Bn, i.e., the join $${K_2} \vee \overline {{K_n}} $$. Erdős, Faudree, Rousseau and Schelp proved that Tn is Bm-good if $$n \ge 3m - 3$$. In this paper, we obtain the exact Ramsey number of Tn versus 2B2- Our result implies that Tn is 2B2-good if n ≥ 5. © The Editorial Office of AMAS & Springer-Verlag GmbH Germany 2024 |
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Ramsey Numbers of Trees Versus Multiple Copies of Books |
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| score |
7.3996143 |