Hamiltonicity of 3-tough $(K_2 \cup 3K_1)$-free graphs
Combinatorics
2021-06-15 v1
Abstract
Chv\'{a}tal conjectured in 1973 the existence of some constant such that all -tough graphs with at least three vertices are hamiltonian. While the conjecture has been proven for some special classes of graphs, it remains open in general. We say that a graph is -free if it contains no induced subgraph isomorphic to , where is the disjoint union of an edge and three isolated vertices. In this paper, we show that every 3-tough -free graph with at least three vertices is hamiltonian.
Cite
@article{arxiv.2106.07083,
title = {Hamiltonicity of 3-tough $(K_2 \cup 3K_1)$-free graphs},
author = {Andrew Hatfield and Elizabeth Grimm},
journal= {arXiv preprint arXiv:2106.07083},
year = {2021}
}