2-韧化$2K_2$-自由图中的哈密顿圈
组合数学
2021-12-06 v3
摘要
若图不包含作为诱导子图，则称其为-自由图。2014年，Broersma、Patel和Pyatkin证明每个至少三个顶点的25-韧化-自由图是哈密顿图。最近，Shan改进了该结果，证明3-韧化已足够，而非25-韧化。在本文中，我们证明每个至少三个顶点的2-韧化-自由图是哈密顿图，这是Gao和Pasechnik所猜想的。
引用
@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}
}
备注
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. $ \ $