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A note on cycle lengths in graphs of chromatic number five and six

Autor: Huo, Qingyi

In this note, we prove that every non-complete $(k+1)$-critical graph contains cycles of all lengths modulo $k$, where $k=4,5$.
Comment: arXiv admin note: text overlap with arXiv:2012.10624

Externí odkaz: http://arxiv.org/abs/2104.01382

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A strengthening on odd cycles in graphs of given chromatic number

Autor: Gao, Jun, Huo, Qingyi, Ma, Jie

Resolving a conjecture of Bollob\'{a}s and Erd\H{o}s, Gy\'{a}rf\'{a}s proved that every graph $G$ of chromatic number $k+1\geq 3$ contains cycles of $\lfloor\frac{k}{2}\rfloor$ distinct odd lengths. We strengthen this prominent result by showing that

Externí odkaz: http://arxiv.org/abs/2012.10624

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A unified proof of conjectures on cycle lengths in graphs

Autor: Gao, Jun, Huo, Qingyi, Liu, Chun-Hung, Ma, Jie

In this paper, we prove a tight minimum degree condition in general graphs for the existence of paths between two given endpoints, whose lengths form a long arithmetic progression with common difference one or two. This allows us to obtain a number o

Externí odkaz: http://arxiv.org/abs/1904.08126

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