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- W3114150241 abstract "Resolving a conjecture of Bollob'{a}s and ErdH{o}s, Gy'{a}rf'{a}s proved that every graph $G$ of chromatic number $k+1geq 3$ contains cycles of $lfloorfrac{k}{2}rfloor$ distinct odd lengths. We strengthen this prominent result by showing that such $G$ contains cycles of $lfloorfrac{k}{2}rfloor$ consecutive odd lengths. Along the way, combining extremal and structural tools, we prove a stronger statement that every graph of chromatic number $k+1geq 7$ contains $k$ cycles of consecutive lengths, except that some block is $K_{k+1}$. As corollaries, this confirms a conjecture of Verstraete and answers a question of Moore and West." @default.
- W3114150241 created "2021-01-05" @default.
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- W3114150241 date "2020-12-19" @default.
- W3114150241 modified "2023-09-27" @default.
- W3114150241 title "A strengthening on odd cycles in graphs of given chromatic number" @default.
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- W3114150241 doi "https://doi.org/10.48550/arxiv.2012.10624" @default.
- W3114150241 hasPublicationYear "2020" @default.
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