Erd\H{o}s-Gy\'arf\'as conjecture on graphs without long induced paths
In 1994, Erd\H{o}s and Gy\'arf\'as conjectured that every graph with minimum degree at least 3 has a cycle of length a power of 2. In 2022, Gao and Shan (Graphs and Combinatorics) proved that the conjecture is true for $P_8$-free graphs, i.e., graphs without any induced copies of a path on...
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| creator | Hegde, Anand Shripad Sandeep, R. B Shashank, P |
| description | In 1994, Erd\H{o}s and Gy\'arf\'as conjectured that every graph with minimum
degree at least 3 has a cycle of length a power of 2. In 2022, Gao and Shan
(Graphs and Combinatorics) proved that the conjecture is true for $P_8$-free
graphs, i.e., graphs without any induced copies of a path on 8 vertices. In
2024, Hu and Shen (Discrete Mathematics) improved this result by proving that
the conjecture is true for $P_{10}$-free graphs. With the aid of a computer
search, we improve this further by proving that the conjecture is true for
$P_{13}$-free graphs. |
| doi_str_mv | 10.48550/arxiv.2410.22842 |
| format | Article |
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degree at least 3 has a cycle of length a power of 2. In 2022, Gao and Shan
(Graphs and Combinatorics) proved that the conjecture is true for $P_8$-free
graphs, i.e., graphs without any induced copies of a path on 8 vertices. In
2024, Hu and Shen (Discrete Mathematics) improved this result by proving that
the conjecture is true for $P_{10}$-free graphs. With the aid of a computer
search, we improve this further by proving that the conjecture is true for
$P_{13}$-free graphs.</description><identifier>DOI: 10.48550/arxiv.2410.22842</identifier><language>eng</language><subject>Computer Science - Data Structures and Algorithms ; Mathematics - Combinatorics</subject><creationdate>2024-10</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2410.22842$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2410.22842$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Hegde, Anand Shripad</creatorcontrib><creatorcontrib>Sandeep, R. B</creatorcontrib><creatorcontrib>Shashank, P</creatorcontrib><title>Erd\H{o}s-Gy\'arf\'as conjecture on graphs without long induced paths</title><description>In 1994, Erd\H{o}s and Gy\'arf\'as conjectured that every graph with minimum
degree at least 3 has a cycle of length a power of 2. In 2022, Gao and Shan
(Graphs and Combinatorics) proved that the conjecture is true for $P_8$-free
graphs, i.e., graphs without any induced copies of a path on 8 vertices. In
2024, Hu and Shen (Discrete Mathematics) improved this result by proving that
the conjecture is true for $P_{10}$-free graphs. With the aid of a computer
search, we improve this further by proving that the conjecture is true for
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degree at least 3 has a cycle of length a power of 2. In 2022, Gao and Shan
(Graphs and Combinatorics) proved that the conjecture is true for $P_8$-free
graphs, i.e., graphs without any induced copies of a path on 8 vertices. In
2024, Hu and Shen (Discrete Mathematics) improved this result by proving that
the conjecture is true for $P_{10}$-free graphs. With the aid of a computer
search, we improve this further by proving that the conjecture is true for
$P_{13}$-free graphs.</abstract><doi>10.48550/arxiv.2410.22842</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Data Structures and Algorithms Mathematics - Combinatorics |
| title | Erd\H{o}s-Gy\'arf\'as conjecture on graphs without long induced paths |
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