Hamiltonian cycles in 2-tough $2K_2$-free graphs
Abstract
A graph is called a -free graph if it does not contain as an induced subgraph. In 2014, Broersma, Patel and Pyatkin showed that every 25-tough -free graph on at least three vertices is Hamiltonian. Recently, Shan improved this result by showing that 3-tough is sufficient instead of 25-tough. In this paper, we show that every 2-tough -free graph on at least three vertices is Hamiltonian, which was conjectured by Gao and Pasechnik.
Keywords
Cite
@article{arxiv.2103.06760,
title = {Hamiltonian cycles in 2-tough $2K_2$-free graphs},
author = {Katsuhiro Ota and Masahiro Sanka},
journal= {arXiv preprint arXiv:2103.06760},
year = {2021}
}
Comments
14 pages. We have noticed that one of our results, showing that every $\frac{3}{2}$-tough $2K_2$-free graph on at least three vertices has a 2-factor, is an immediate corollary to a known result. So, we have just described the result on 2-factors as a proposition, and have omitted our proof (Section 3 in the previous version) in the paper. Accordingly, we have changed the title. $ \ $