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arXiv · 1109.4675

Heavy subgraph conditions for longest cycles to be heavy in graphs

Binlong Li·Shenggui Zhang
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Abstract

Let $G$ be a graph on $n$ vertices. A vertex of $G$ with degree at least $n/2$ is called a heavy vertex, and a cycle of $G$ which contains all the heavy vertices of $G$ is called a heavy cycle. In this paper, we characterize the graphs which contain no heavy cycles. For a given graph $H$, we say that $G$ is $H$-\emph{heavy} if every induced subgraph of $G$ isomorphic to $H$ contains two nonadjacent vertices with degree sum at least $n$. We find all the connected graphs $S$ such that a 2-connected graph $G$ being $S$-heavy implies any longest cycle of $G$ is a heavy cycle.

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Binlong Li, Shenggui Zhang. 2011-09-21. Heavy subgraph conditions for longest cycles to be heavy in graphs. https://arxiv.org/abs/1109.4675

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