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arXiv · 2306.12579

Pancyclicity of highly connected graphs

Shoham Letzter
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Abstract

A well-known result due to Chvatál and Erdős (1972) asserts that, if a graph $G$ satisfies $κ(G) \ge α(G)$, where $κ(G)$ is the vertex-connectivity of $G$, then $G$ has a Hamilton cycle. We prove a similar result implying that a graph $G$ is pancyclic, namely it contains cycles of all lengths between $3$ and $|G|$: if $|G|$ is large and $κ(G) > α(G)$, then $G$ is pancyclic. This confirms a conjecture of Jackson and Ordaz (1990) for large graphs, and improves upon a very recent result of Draganić, Munhá-Correia, and Sudakov.

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Shoham Letzter. 2026-06-29. Pancyclicity of highly connected graphs. https://arxiv.org/abs/2306.12579

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