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arXiv · 2506.12684

Hamilton cycles in tough $(2P_2 \cup P_1)$-free graphs

Songling Shan·Arthur Tanyel
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Abstract

In 1973, Chvátal conjectured that there exists a constant $t_0$ such that every $t_0$-tough graph on at least three vertices is Hamiltonian. While this conjecture is still open, work has been done to confirm it for several graph classes, including all $F$-free graphs for every 5-vertex linear forest $F$ other than $P_5$ and $2P_2\cup P_1$. In this note, we show that 11-tough $(2P_2 \cup P_1)$-free graphs on at least three vertices are Hamiltonian.

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BibTeXRIS

Songling Shan, Arthur Tanyel. 2025-06-15. Hamilton cycles in tough $(2P_2 \cup P_1)$-free graphs. https://arxiv.org/abs/2506.12684

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