论文信息 - Forbidden Subgraphs for Hamiltonicity of 1-Tough Graphs

Forbidden Subgraphs for Hamiltonicity of 1-Tough Graphs

Abstract A graph G is said to be 1-tough if for every vertex cut S of G, the number of components of G − S does not exceed |S|. Being 1-tough is an obvious necessary condition for a graph to be hamiltonian, but it is not sufficient in general. We study the problem of characterizing all graphs H such that every 1-tough H-free graph is hamiltonian. We almost obtain a complete solution to this problem, leaving H = K1 ∪ P4 as the only open case.

Shenggui Zhang | Binlong Li | Hajo Broersma

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