Path Factors and Neighborhoods of Independent Sets in Graphs
Abstract A path-factor is a spanning subgraph F of G such that every component of F is a path with at least two vertices. Let k ≥ 2 be an integer. A P≥k-factor of G means a path factor in which each component is a path with at least k vertices. A graph G is a P≥k-factor covered graph if for any e ∈...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Zhou, Si-zhong [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 2023 |
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| Übergeordnetes Werk: |
Enthalten in: Acta mathematicae applicatae sinica - Berlin : Springer, 1984, 39(2023), 2 vom: Apr., Seite 232-238 |
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| Übergeordnetes Werk: |
volume:39 ; year:2023 ; number:2 ; month:04 ; pages:232-238 |
| Links: |
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| DOI / URN: |
10.1007/s10255-022-1096-2 |
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| Katalog-ID: |
SPR050106163 |
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| 100 | 1 | |a Zhou, Si-zhong |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Path Factors and Neighborhoods of Independent Sets in Graphs |
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| 520 | |a Abstract A path-factor is a spanning subgraph F of G such that every component of F is a path with at least two vertices. Let k ≥ 2 be an integer. A P≥k-factor of G means a path factor in which each component is a path with at least k vertices. A graph G is a P≥k-factor covered graph if for any e ∈ E(G), G has a P≥k-factor including e. Let β be a real number with %${{1 \over 3}}\leq\beta\leq 1%$ and k be a positive integer. We verify that (i) a k-connected graph G of order n with n ≥ 5k + 2 has a P≥3-factor if ∣NG(I)∣ > β(n−3k − 1) + k for every independent set I of G with ∣I∣ = ⌊β(2k + 1)⌋; (ii) a (k + 1)-connected graph G of order n with n ≥ 5k + 2 is a P≥3-factor covered graph if ∣NG(I)∣ > β(n − 3k − 1) + k + 1 for every independent set I of G with ∣I∣ = ⌊β(2k + 1)⌋. | ||
| 650 | 4 | |a graph |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a independent set |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a neighborhood |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a -factor |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a -factor covered graph |7 (dpeaa)DE-He213 | |
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10.1007/s10255-022-1096-2 doi (DE-627)SPR050106163 (SPR)s10255-022-1096-2-e DE-627 ger DE-627 rakwb eng Zhou, Si-zhong verfasserin aut Path Factors and Neighborhoods of Independent Sets in Graphs 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Editorial Office of AMAS & Springer-Verlag GmbH Germany 2023 Abstract A path-factor is a spanning subgraph F of G such that every component of F is a path with at least two vertices. Let k ≥ 2 be an integer. A P≥k-factor of G means a path factor in which each component is a path with at least k vertices. A graph G is a P≥k-factor covered graph if for any e ∈ E(G), G has a P≥k-factor including e. Let β be a real number with %${{1 \over 3}}\leq\beta\leq 1%$ and k be a positive integer. We verify that (i) a k-connected graph G of order n with n ≥ 5k + 2 has a P≥3-factor if ∣NG(I)∣ > β(n−3k − 1) + k for every independent set I of G with ∣I∣ = ⌊β(2k + 1)⌋; (ii) a (k + 1)-connected graph G of order n with n ≥ 5k + 2 is a P≥3-factor covered graph if ∣NG(I)∣ > β(n − 3k − 1) + k + 1 for every independent set I of G with ∣I∣ = ⌊β(2k + 1)⌋. graph (dpeaa)DE-He213 independent set (dpeaa)DE-He213 neighborhood (dpeaa)DE-He213 -factor (dpeaa)DE-He213 -factor covered graph (dpeaa)DE-He213 Enthalten in Acta mathematicae applicatae sinica Berlin : Springer, 1984 39(2023), 2 vom: Apr., Seite 232-238 (DE-627)345617312 (DE-600)2076073-5 1618-3932 nnns volume:39 year:2023 number:2 month:04 pages:232-238 https://dx.doi.org/10.1007/s10255-022-1096-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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 AR 39 2023 2 04 232-238 |
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10.1007/s10255-022-1096-2 doi (DE-627)SPR050106163 (SPR)s10255-022-1096-2-e DE-627 ger DE-627 rakwb eng Zhou, Si-zhong verfasserin aut Path Factors and Neighborhoods of Independent Sets in Graphs 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Editorial Office of AMAS & Springer-Verlag GmbH Germany 2023 Abstract A path-factor is a spanning subgraph F of G such that every component of F is a path with at least two vertices. Let k ≥ 2 be an integer. A P≥k-factor of G means a path factor in which each component is a path with at least k vertices. A graph G is a P≥k-factor covered graph if for any e ∈ E(G), G has a P≥k-factor including e. Let β be a real number with %${{1 \over 3}}\leq\beta\leq 1%$ and k be a positive integer. We verify that (i) a k-connected graph G of order n with n ≥ 5k + 2 has a P≥3-factor if ∣NG(I)∣ > β(n−3k − 1) + k for every independent set I of G with ∣I∣ = ⌊β(2k + 1)⌋; (ii) a (k + 1)-connected graph G of order n with n ≥ 5k + 2 is a P≥3-factor covered graph if ∣NG(I)∣ > β(n − 3k − 1) + k + 1 for every independent set I of G with ∣I∣ = ⌊β(2k + 1)⌋. graph (dpeaa)DE-He213 independent set (dpeaa)DE-He213 neighborhood (dpeaa)DE-He213 -factor (dpeaa)DE-He213 -factor covered graph (dpeaa)DE-He213 Enthalten in Acta mathematicae applicatae sinica Berlin : Springer, 1984 39(2023), 2 vom: Apr., Seite 232-238 (DE-627)345617312 (DE-600)2076073-5 1618-3932 nnns volume:39 year:2023 number:2 month:04 pages:232-238 https://dx.doi.org/10.1007/s10255-022-1096-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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 AR 39 2023 2 04 232-238 |
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10.1007/s10255-022-1096-2 doi (DE-627)SPR050106163 (SPR)s10255-022-1096-2-e DE-627 ger DE-627 rakwb eng Zhou, Si-zhong verfasserin aut Path Factors and Neighborhoods of Independent Sets in Graphs 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Editorial Office of AMAS & Springer-Verlag GmbH Germany 2023 Abstract A path-factor is a spanning subgraph F of G such that every component of F is a path with at least two vertices. Let k ≥ 2 be an integer. A P≥k-factor of G means a path factor in which each component is a path with at least k vertices. A graph G is a P≥k-factor covered graph if for any e ∈ E(G), G has a P≥k-factor including e. Let β be a real number with %${{1 \over 3}}\leq\beta\leq 1%$ and k be a positive integer. We verify that (i) a k-connected graph G of order n with n ≥ 5k + 2 has a P≥3-factor if ∣NG(I)∣ > β(n−3k − 1) + k for every independent set I of G with ∣I∣ = ⌊β(2k + 1)⌋; (ii) a (k + 1)-connected graph G of order n with n ≥ 5k + 2 is a P≥3-factor covered graph if ∣NG(I)∣ > β(n − 3k − 1) + k + 1 for every independent set I of G with ∣I∣ = ⌊β(2k + 1)⌋. graph (dpeaa)DE-He213 independent set (dpeaa)DE-He213 neighborhood (dpeaa)DE-He213 -factor (dpeaa)DE-He213 -factor covered graph (dpeaa)DE-He213 Enthalten in Acta mathematicae applicatae sinica Berlin : Springer, 1984 39(2023), 2 vom: Apr., Seite 232-238 (DE-627)345617312 (DE-600)2076073-5 1618-3932 nnns volume:39 year:2023 number:2 month:04 pages:232-238 https://dx.doi.org/10.1007/s10255-022-1096-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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 AR 39 2023 2 04 232-238 |
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10.1007/s10255-022-1096-2 doi (DE-627)SPR050106163 (SPR)s10255-022-1096-2-e DE-627 ger DE-627 rakwb eng Zhou, Si-zhong verfasserin aut Path Factors and Neighborhoods of Independent Sets in Graphs 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Editorial Office of AMAS & Springer-Verlag GmbH Germany 2023 Abstract A path-factor is a spanning subgraph F of G such that every component of F is a path with at least two vertices. Let k ≥ 2 be an integer. A P≥k-factor of G means a path factor in which each component is a path with at least k vertices. A graph G is a P≥k-factor covered graph if for any e ∈ E(G), G has a P≥k-factor including e. Let β be a real number with %${{1 \over 3}}\leq\beta\leq 1%$ and k be a positive integer. We verify that (i) a k-connected graph G of order n with n ≥ 5k + 2 has a P≥3-factor if ∣NG(I)∣ > β(n−3k − 1) + k for every independent set I of G with ∣I∣ = ⌊β(2k + 1)⌋; (ii) a (k + 1)-connected graph G of order n with n ≥ 5k + 2 is a P≥3-factor covered graph if ∣NG(I)∣ > β(n − 3k − 1) + k + 1 for every independent set I of G with ∣I∣ = ⌊β(2k + 1)⌋. graph (dpeaa)DE-He213 independent set (dpeaa)DE-He213 neighborhood (dpeaa)DE-He213 -factor (dpeaa)DE-He213 -factor covered graph (dpeaa)DE-He213 Enthalten in Acta mathematicae applicatae sinica Berlin : Springer, 1984 39(2023), 2 vom: Apr., Seite 232-238 (DE-627)345617312 (DE-600)2076073-5 1618-3932 nnns volume:39 year:2023 number:2 month:04 pages:232-238 https://dx.doi.org/10.1007/s10255-022-1096-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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 AR 39 2023 2 04 232-238 |
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10.1007/s10255-022-1096-2 doi (DE-627)SPR050106163 (SPR)s10255-022-1096-2-e DE-627 ger DE-627 rakwb eng Zhou, Si-zhong verfasserin aut Path Factors and Neighborhoods of Independent Sets in Graphs 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Editorial Office of AMAS & Springer-Verlag GmbH Germany 2023 Abstract A path-factor is a spanning subgraph F of G such that every component of F is a path with at least two vertices. Let k ≥ 2 be an integer. A P≥k-factor of G means a path factor in which each component is a path with at least k vertices. A graph G is a P≥k-factor covered graph if for any e ∈ E(G), G has a P≥k-factor including e. Let β be a real number with %${{1 \over 3}}\leq\beta\leq 1%$ and k be a positive integer. We verify that (i) a k-connected graph G of order n with n ≥ 5k + 2 has a P≥3-factor if ∣NG(I)∣ > β(n−3k − 1) + k for every independent set I of G with ∣I∣ = ⌊β(2k + 1)⌋; (ii) a (k + 1)-connected graph G of order n with n ≥ 5k + 2 is a P≥3-factor covered graph if ∣NG(I)∣ > β(n − 3k − 1) + k + 1 for every independent set I of G with ∣I∣ = ⌊β(2k + 1)⌋. graph (dpeaa)DE-He213 independent set (dpeaa)DE-He213 neighborhood (dpeaa)DE-He213 -factor (dpeaa)DE-He213 -factor covered graph (dpeaa)DE-He213 Enthalten in Acta mathematicae applicatae sinica Berlin : Springer, 1984 39(2023), 2 vom: Apr., Seite 232-238 (DE-627)345617312 (DE-600)2076073-5 1618-3932 nnns volume:39 year:2023 number:2 month:04 pages:232-238 https://dx.doi.org/10.1007/s10255-022-1096-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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 AR 39 2023 2 04 232-238 |
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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">SPR050106163</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230420064700.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">230420s2023 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10255-022-1096-2</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR050106163</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s10255-022-1096-2-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="100" ind1="1" ind2=" "><subfield code="a">Zhou, Si-zhong</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Path Factors and Neighborhoods of Independent Sets in Graphs</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 2023</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract A path-factor is a spanning subgraph F of G such that every component of F is a path with at least two vertices. Let k ≥ 2 be an integer. A P≥k-factor of G means a path factor in which each component is a path with at least k vertices. A graph G is a P≥k-factor covered graph if for any e ∈ E(G), G has a P≥k-factor including e. Let β be a real number with %${{1 \over 3}}\leq\beta\leq 1%$ and k be a positive integer. We verify that (i) a k-connected graph G of order n with n ≥ 5k + 2 has a P≥3-factor if ∣NG(I)∣ > β(n−3k − 1) + k for every independent set I of G with ∣I∣ = ⌊β(2k + 1)⌋; (ii) a (k + 1)-connected graph G of order n with n ≥ 5k + 2 is a P≥3-factor covered graph if ∣NG(I)∣ > β(n − 3k − 1) + k + 1 for every independent set I of G with ∣I∣ = ⌊β(2k + 1)⌋.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">graph</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">independent set</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">neighborhood</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">-factor</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">-factor covered 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|
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Zhou, Si-zhong |
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Zhou, Si-zhong misc graph misc independent set misc neighborhood misc -factor misc -factor covered graph Path Factors and Neighborhoods of Independent Sets in Graphs |
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Path Factors and Neighborhoods of Independent Sets in Graphs graph (dpeaa)DE-He213 independent set (dpeaa)DE-He213 neighborhood (dpeaa)DE-He213 -factor (dpeaa)DE-He213 -factor covered graph (dpeaa)DE-He213 |
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misc graph misc independent set misc neighborhood misc -factor misc -factor covered graph |
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misc graph misc independent set misc neighborhood misc -factor misc -factor covered graph |
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Elektronische Aufsätze Aufsätze Elektronische Ressource |
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Path Factors and Neighborhoods of Independent Sets in Graphs |
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Path Factors and Neighborhoods of Independent Sets in Graphs |
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Zhou, Si-zhong |
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Acta mathematicae applicatae sinica |
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Acta mathematicae applicatae sinica |
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Elektronische Aufsätze |
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10.1007/s10255-022-1096-2 |
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path factors and neighborhoods of independent sets in graphs |
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Path Factors and Neighborhoods of Independent Sets in Graphs |
| abstract |
Abstract A path-factor is a spanning subgraph F of G such that every component of F is a path with at least two vertices. Let k ≥ 2 be an integer. A P≥k-factor of G means a path factor in which each component is a path with at least k vertices. A graph G is a P≥k-factor covered graph if for any e ∈ E(G), G has a P≥k-factor including e. Let β be a real number with %${{1 \over 3}}\leq\beta\leq 1%$ and k be a positive integer. We verify that (i) a k-connected graph G of order n with n ≥ 5k + 2 has a P≥3-factor if ∣NG(I)∣ > β(n−3k − 1) + k for every independent set I of G with ∣I∣ = ⌊β(2k + 1)⌋; (ii) a (k + 1)-connected graph G of order n with n ≥ 5k + 2 is a P≥3-factor covered graph if ∣NG(I)∣ > β(n − 3k − 1) + k + 1 for every independent set I of G with ∣I∣ = ⌊β(2k + 1)⌋. © The Editorial Office of AMAS & Springer-Verlag GmbH Germany 2023 |
| abstractGer |
Abstract A path-factor is a spanning subgraph F of G such that every component of F is a path with at least two vertices. Let k ≥ 2 be an integer. A P≥k-factor of G means a path factor in which each component is a path with at least k vertices. A graph G is a P≥k-factor covered graph if for any e ∈ E(G), G has a P≥k-factor including e. Let β be a real number with %${{1 \over 3}}\leq\beta\leq 1%$ and k be a positive integer. We verify that (i) a k-connected graph G of order n with n ≥ 5k + 2 has a P≥3-factor if ∣NG(I)∣ > β(n−3k − 1) + k for every independent set I of G with ∣I∣ = ⌊β(2k + 1)⌋; (ii) a (k + 1)-connected graph G of order n with n ≥ 5k + 2 is a P≥3-factor covered graph if ∣NG(I)∣ > β(n − 3k − 1) + k + 1 for every independent set I of G with ∣I∣ = ⌊β(2k + 1)⌋. © The Editorial Office of AMAS & Springer-Verlag GmbH Germany 2023 |
| abstract_unstemmed |
Abstract A path-factor is a spanning subgraph F of G such that every component of F is a path with at least two vertices. Let k ≥ 2 be an integer. A P≥k-factor of G means a path factor in which each component is a path with at least k vertices. A graph G is a P≥k-factor covered graph if for any e ∈ E(G), G has a P≥k-factor including e. Let β be a real number with %${{1 \over 3}}\leq\beta\leq 1%$ and k be a positive integer. We verify that (i) a k-connected graph G of order n with n ≥ 5k + 2 has a P≥3-factor if ∣NG(I)∣ > β(n−3k − 1) + k for every independent set I of G with ∣I∣ = ⌊β(2k + 1)⌋; (ii) a (k + 1)-connected graph G of order n with n ≥ 5k + 2 is a P≥3-factor covered graph if ∣NG(I)∣ > β(n − 3k − 1) + k + 1 for every independent set I of G with ∣I∣ = ⌊β(2k + 1)⌋. © The Editorial Office of AMAS & Springer-Verlag GmbH Germany 2023 |
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| container_issue |
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| title_short |
Path Factors and Neighborhoods of Independent Sets in Graphs |
| url |
https://dx.doi.org/10.1007/s10255-022-1096-2 |
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10.1007/s10255-022-1096-2 |
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2024-07-03T13:25:06.996Z |
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| score |
7.3998156 |