Burning Graph Classes
Abstract The Burning Number Conjecture, that a graph on n vertices can be burned in at most $$\lceil \sqrt{n} \ \rceil $$ rounds, has been of central interest for the past several years. Much of the literature toward its resolution focuses on two directions: tightening a general upper bound for the...
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| Autor*in: |
Omar, Mohamed [verfasserIn] |
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Artikel |
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Englisch |
| Erschienen: |
2022 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature 2022 |
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| Übergeordnetes Werk: |
Enthalten in: Graphs and combinatorics - Springer Japan, 1985, 38(2022), 4 vom: 19. Juli |
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volume:38 ; year:2022 ; number:4 ; day:19 ; month:07 |
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10.1007/s00373-022-02523-w |
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| 520 | |a Abstract The Burning Number Conjecture, that a graph on n vertices can be burned in at most $$\lceil \sqrt{n} \ \rceil $$ rounds, has been of central interest for the past several years. Much of the literature toward its resolution focuses on two directions: tightening a general upper bound for the burning number, and proving the conjecture for specific graph classes. In the latter, most of the developments work within a specific graph class and exploit the intricacies particular to it. In this article, we broaden this approach by developing systematic machinery that can be used as test beds for asserting that graph classes satisfy the conjecture. We show how to use these to resolve the conjecture for several classes of graphs including triangle-free graphs with degree lower bounds, graphs with certain linear lower bounds on r-neighborhood sizes, all trees whose non-leaf vertices have degree at least 4, trees whose non-leaf vertices have degree at least 3 (on at least 81 vertices), trees whose non-leaf vertices are less than $$\frac{2}{3}$$ concentrated in degree 2, and trees with a low concentration of high degree non-leaf vertices (the last two results holding for sufficiently many non-leaf vertices). | ||
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10.1007/s00373-022-02523-w doi (DE-627)OLC2079186825 (DE-He213)s00373-022-02523-w-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Omar, Mohamed verfasserin aut Burning Graph Classes 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature 2022 Abstract The Burning Number Conjecture, that a graph on n vertices can be burned in at most $$\lceil \sqrt{n} \ \rceil $$ rounds, has been of central interest for the past several years. Much of the literature toward its resolution focuses on two directions: tightening a general upper bound for the burning number, and proving the conjecture for specific graph classes. In the latter, most of the developments work within a specific graph class and exploit the intricacies particular to it. In this article, we broaden this approach by developing systematic machinery that can be used as test beds for asserting that graph classes satisfy the conjecture. We show how to use these to resolve the conjecture for several classes of graphs including triangle-free graphs with degree lower bounds, graphs with certain linear lower bounds on r-neighborhood sizes, all trees whose non-leaf vertices have degree at least 4, trees whose non-leaf vertices have degree at least 3 (on at least 81 vertices), trees whose non-leaf vertices are less than $$\frac{2}{3}$$ concentrated in degree 2, and trees with a low concentration of high degree non-leaf vertices (the last two results holding for sufficiently many non-leaf vertices). Graphs Burning number Trees Graph neighborhood Rohilla, Vibha aut Enthalten in Graphs and combinatorics Springer Japan, 1985 38(2022), 4 vom: 19. Juli (DE-627)129274453 (DE-600)84314-3 (DE-576)014463903 0911-0119 nnns volume:38 year:2022 number:4 day:19 month:07 https://doi.org/10.1007/s00373-022-02523-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2018 AR 38 2022 4 19 07 |
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10.1007/s00373-022-02523-w doi (DE-627)OLC2079186825 (DE-He213)s00373-022-02523-w-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Omar, Mohamed verfasserin aut Burning Graph Classes 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature 2022 Abstract The Burning Number Conjecture, that a graph on n vertices can be burned in at most $$\lceil \sqrt{n} \ \rceil $$ rounds, has been of central interest for the past several years. Much of the literature toward its resolution focuses on two directions: tightening a general upper bound for the burning number, and proving the conjecture for specific graph classes. In the latter, most of the developments work within a specific graph class and exploit the intricacies particular to it. In this article, we broaden this approach by developing systematic machinery that can be used as test beds for asserting that graph classes satisfy the conjecture. We show how to use these to resolve the conjecture for several classes of graphs including triangle-free graphs with degree lower bounds, graphs with certain linear lower bounds on r-neighborhood sizes, all trees whose non-leaf vertices have degree at least 4, trees whose non-leaf vertices have degree at least 3 (on at least 81 vertices), trees whose non-leaf vertices are less than $$\frac{2}{3}$$ concentrated in degree 2, and trees with a low concentration of high degree non-leaf vertices (the last two results holding for sufficiently many non-leaf vertices). Graphs Burning number Trees Graph neighborhood Rohilla, Vibha aut Enthalten in Graphs and combinatorics Springer Japan, 1985 38(2022), 4 vom: 19. Juli (DE-627)129274453 (DE-600)84314-3 (DE-576)014463903 0911-0119 nnns volume:38 year:2022 number:4 day:19 month:07 https://doi.org/10.1007/s00373-022-02523-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2018 AR 38 2022 4 19 07 |
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10.1007/s00373-022-02523-w doi (DE-627)OLC2079186825 (DE-He213)s00373-022-02523-w-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Omar, Mohamed verfasserin aut Burning Graph Classes 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature 2022 Abstract The Burning Number Conjecture, that a graph on n vertices can be burned in at most $$\lceil \sqrt{n} \ \rceil $$ rounds, has been of central interest for the past several years. Much of the literature toward its resolution focuses on two directions: tightening a general upper bound for the burning number, and proving the conjecture for specific graph classes. In the latter, most of the developments work within a specific graph class and exploit the intricacies particular to it. In this article, we broaden this approach by developing systematic machinery that can be used as test beds for asserting that graph classes satisfy the conjecture. We show how to use these to resolve the conjecture for several classes of graphs including triangle-free graphs with degree lower bounds, graphs with certain linear lower bounds on r-neighborhood sizes, all trees whose non-leaf vertices have degree at least 4, trees whose non-leaf vertices have degree at least 3 (on at least 81 vertices), trees whose non-leaf vertices are less than $$\frac{2}{3}$$ concentrated in degree 2, and trees with a low concentration of high degree non-leaf vertices (the last two results holding for sufficiently many non-leaf vertices). Graphs Burning number Trees Graph neighborhood Rohilla, Vibha aut Enthalten in Graphs and combinatorics Springer Japan, 1985 38(2022), 4 vom: 19. Juli (DE-627)129274453 (DE-600)84314-3 (DE-576)014463903 0911-0119 nnns volume:38 year:2022 number:4 day:19 month:07 https://doi.org/10.1007/s00373-022-02523-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2018 AR 38 2022 4 19 07 |
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10.1007/s00373-022-02523-w doi (DE-627)OLC2079186825 (DE-He213)s00373-022-02523-w-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Omar, Mohamed verfasserin aut Burning Graph Classes 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature 2022 Abstract The Burning Number Conjecture, that a graph on n vertices can be burned in at most $$\lceil \sqrt{n} \ \rceil $$ rounds, has been of central interest for the past several years. Much of the literature toward its resolution focuses on two directions: tightening a general upper bound for the burning number, and proving the conjecture for specific graph classes. In the latter, most of the developments work within a specific graph class and exploit the intricacies particular to it. In this article, we broaden this approach by developing systematic machinery that can be used as test beds for asserting that graph classes satisfy the conjecture. We show how to use these to resolve the conjecture for several classes of graphs including triangle-free graphs with degree lower bounds, graphs with certain linear lower bounds on r-neighborhood sizes, all trees whose non-leaf vertices have degree at least 4, trees whose non-leaf vertices have degree at least 3 (on at least 81 vertices), trees whose non-leaf vertices are less than $$\frac{2}{3}$$ concentrated in degree 2, and trees with a low concentration of high degree non-leaf vertices (the last two results holding for sufficiently many non-leaf vertices). Graphs Burning number Trees Graph neighborhood Rohilla, Vibha aut Enthalten in Graphs and combinatorics Springer Japan, 1985 38(2022), 4 vom: 19. Juli (DE-627)129274453 (DE-600)84314-3 (DE-576)014463903 0911-0119 nnns volume:38 year:2022 number:4 day:19 month:07 https://doi.org/10.1007/s00373-022-02523-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2018 AR 38 2022 4 19 07 |
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10.1007/s00373-022-02523-w doi (DE-627)OLC2079186825 (DE-He213)s00373-022-02523-w-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Omar, Mohamed verfasserin aut Burning Graph Classes 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature 2022 Abstract The Burning Number Conjecture, that a graph on n vertices can be burned in at most $$\lceil \sqrt{n} \ \rceil $$ rounds, has been of central interest for the past several years. Much of the literature toward its resolution focuses on two directions: tightening a general upper bound for the burning number, and proving the conjecture for specific graph classes. In the latter, most of the developments work within a specific graph class and exploit the intricacies particular to it. In this article, we broaden this approach by developing systematic machinery that can be used as test beds for asserting that graph classes satisfy the conjecture. We show how to use these to resolve the conjecture for several classes of graphs including triangle-free graphs with degree lower bounds, graphs with certain linear lower bounds on r-neighborhood sizes, all trees whose non-leaf vertices have degree at least 4, trees whose non-leaf vertices have degree at least 3 (on at least 81 vertices), trees whose non-leaf vertices are less than $$\frac{2}{3}$$ concentrated in degree 2, and trees with a low concentration of high degree non-leaf vertices (the last two results holding for sufficiently many non-leaf vertices). Graphs Burning number Trees Graph neighborhood Rohilla, Vibha aut Enthalten in Graphs and combinatorics Springer Japan, 1985 38(2022), 4 vom: 19. Juli (DE-627)129274453 (DE-600)84314-3 (DE-576)014463903 0911-0119 nnns volume:38 year:2022 number:4 day:19 month:07 https://doi.org/10.1007/s00373-022-02523-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2018 AR 38 2022 4 19 07 |
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Abstract The Burning Number Conjecture, that a graph on n vertices can be burned in at most $$\lceil \sqrt{n} \ \rceil $$ rounds, has been of central interest for the past several years. Much of the literature toward its resolution focuses on two directions: tightening a general upper bound for the burning number, and proving the conjecture for specific graph classes. In the latter, most of the developments work within a specific graph class and exploit the intricacies particular to it. In this article, we broaden this approach by developing systematic machinery that can be used as test beds for asserting that graph classes satisfy the conjecture. We show how to use these to resolve the conjecture for several classes of graphs including triangle-free graphs with degree lower bounds, graphs with certain linear lower bounds on r-neighborhood sizes, all trees whose non-leaf vertices have degree at least 4, trees whose non-leaf vertices have degree at least 3 (on at least 81 vertices), trees whose non-leaf vertices are less than $$\frac{2}{3}$$ concentrated in degree 2, and trees with a low concentration of high degree non-leaf vertices (the last two results holding for sufficiently many non-leaf vertices). © The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature 2022 |
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Abstract The Burning Number Conjecture, that a graph on n vertices can be burned in at most $$\lceil \sqrt{n} \ \rceil $$ rounds, has been of central interest for the past several years. Much of the literature toward its resolution focuses on two directions: tightening a general upper bound for the burning number, and proving the conjecture for specific graph classes. In the latter, most of the developments work within a specific graph class and exploit the intricacies particular to it. In this article, we broaden this approach by developing systematic machinery that can be used as test beds for asserting that graph classes satisfy the conjecture. We show how to use these to resolve the conjecture for several classes of graphs including triangle-free graphs with degree lower bounds, graphs with certain linear lower bounds on r-neighborhood sizes, all trees whose non-leaf vertices have degree at least 4, trees whose non-leaf vertices have degree at least 3 (on at least 81 vertices), trees whose non-leaf vertices are less than $$\frac{2}{3}$$ concentrated in degree 2, and trees with a low concentration of high degree non-leaf vertices (the last two results holding for sufficiently many non-leaf vertices). © The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature 2022 |
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Abstract The Burning Number Conjecture, that a graph on n vertices can be burned in at most $$\lceil \sqrt{n} \ \rceil $$ rounds, has been of central interest for the past several years. Much of the literature toward its resolution focuses on two directions: tightening a general upper bound for the burning number, and proving the conjecture for specific graph classes. In the latter, most of the developments work within a specific graph class and exploit the intricacies particular to it. In this article, we broaden this approach by developing systematic machinery that can be used as test beds for asserting that graph classes satisfy the conjecture. We show how to use these to resolve the conjecture for several classes of graphs including triangle-free graphs with degree lower bounds, graphs with certain linear lower bounds on r-neighborhood sizes, all trees whose non-leaf vertices have degree at least 4, trees whose non-leaf vertices have degree at least 3 (on at least 81 vertices), trees whose non-leaf vertices are less than $$\frac{2}{3}$$ concentrated in degree 2, and trees with a low concentration of high degree non-leaf vertices (the last two results holding for sufficiently many non-leaf vertices). © The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature 2022 |
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| title_short |
Burning Graph Classes |
| url |
https://doi.org/10.1007/s00373-022-02523-w |
| remote_bool |
false |
| author2 |
Rohilla, Vibha |
| author2Str |
Rohilla, Vibha |
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129274453 |
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n |
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| doi_str |
10.1007/s00373-022-02523-w |
| up_date |
2024-07-03T23:52:55.362Z |
| _version_ |
1803603961828081664 |
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