On the pancyclicity of $2$-connected $[5,3]$-graphs

Feng Liu; Hongxi Liu

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arXiv · 2509.20038

On the pancyclicity of $2$-connected $[5,3]$-graphs

Feng Liu·Hongxi Liu

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Abstract

A graph $G$ is called an $[s,t]$-graph if any induced subgraph of $G$ of order $s$ has size at least $t$. In 2024, Zhan conjectured that every $2$-connected $[p + 2, p]$-graph of order at least $2p + 3$ and with minimum degree at least $p$ is pancyclic, where $p$ is an integer with $3 \leq p \leq 5$. In this paper, we confirm the conjecture for the case $p=3$, thereby taking the first step toward a complete resolution of the conjecture.

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Feng Liu, Hongxi Liu. 2025-09-24. On the pancyclicity of $2$-connected $[5,3]$-graphs. https://arxiv.org/abs/2509.20038

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