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arXiv · 1109.4122

Pairs of heavy subgraphs for Hamiltonicity of 2-connected graphs

Binlong Li·Zdeněk Ryjáček·Ying Wang·Shenggui Zhang
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Abstract

Let $G$ be a graph on $n$ vertices. An induced subgraph $H$ of $G$ is called heavy if there exist two nonadjacent vertices in $H$ with degree sum at least $n$ in $G$. We say that $G$ is $H$-heavy if every induced subgraph of $G$ isomorphic to $H$ is heavy. For a family $\mathcal{H}$ of graphs, $G$ is called $\mathcal{H}$-heavy if $G$ is $H$-heavy for every $H\in\mathcal{H}$. In this paper we characterize all connected graphs $R$ and $S$ other than $P_3$ (the path on three vertices) such that every 2-connected $\{R,S\}$-heavy graph is Hamiltonian. This extends several previous results on forbidden subgraph conditions for Hamiltonian graphs.

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Binlong Li, Zdeněk Ryjáček, Ying Wang, Shenggui Zhang. 2011-09-19. Pairs of heavy subgraphs for Hamiltonicity of 2-connected graphs. https://arxiv.org/abs/1109.4122

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