A variation of a theorem by Pósa

Zoltan Furedi; Alexandr Kostochka; Ruth Luo

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arXiv · 1804.05829

A variation of a theorem by Pósa

Zoltan Furedi·Alexandr Kostochka·Ruth Luo

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Abstract

A graph $G$ is $\ell$-hamiltonian if for any linear forest $F$ of $G$ with $\ell$ edges, $F$ can be extended to a hamiltonian cycle of $G$. We give a sharp upper bound for the maximum number of cliques of a fixed size in a non-$\ell$-hamiltonian graph. Furthermore, we prove stability for the bound: if a non-$\ell$-hamiltonian graph contains almost the maximum number of cliques, then it must be a subgraph of one of two examples.

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Zoltan Furedi, Alexandr Kostochka, Ruth Luo. 2018-04-18. A variation of a theorem by Pósa. https://arxiv.org/abs/1804.05829

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