Hamilton cycles in tough $(2P_2 \cup P_1)$-free graphs
Combinatorics
2025-06-17 v1
Abstract
In 1973, Chv\'atal conjectured that there exists a constant such that every -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 -free graphs for every 5-vertex linear forest other than and . In this note, we show that 11-tough -free graphs on at least three vertices are Hamiltonian.
Keywords
Cite
@article{arxiv.2506.12684,
title = {Hamilton cycles in tough $(2P_2 \cup P_1)$-free graphs},
author = {Songling Shan and Arthur Tanyel},
journal= {arXiv preprint arXiv:2506.12684},
year = {2025}
}