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Every 3-connected \(\{K_{1,3},N_{1,2,3}\}\)-free graph is Hamilton-connected

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Abstract

A graph G is \(\{X,Y\}\)-free if it contains neither X nor Y as an induced subgraph. Pairs of connected graphs X, Y such that every 3-connected \(\{X,Y\}\)-free graph is Hamilton-connected have been investigated recently in (2002, 2000, 2012). In this paper, it is shown that every 3-connected \(\{K_{1,3},N_{1,2,3}\}\)-free graph is Hamilton-connected, where \(N_{1,2,3}\) is the graph obtained by identifying end vertices of three disjoint paths of lengths 1, 2, 3 to the vertices of a triangle.

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Acknowledgments

We are very grateful to the referees for their many valuable suggestions and comments.

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Authors and Affiliations

  1. Faculty of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, China

    Zhiquan Hu & Shunzhe Zhang

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  1. Zhiquan Hu
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  2. Shunzhe Zhang
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Correspondence to Shunzhe Zhang.

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Financially supported by NSFC grants 11371062 and 11271149.

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Hu, Z., Zhang, S. Every 3-connected \(\{K_{1,3},N_{1,2,3}\}\)-free graph is Hamilton-connected. Graphs and Combinatorics 32, 685–705 (2016). https://doi.org/10.1007/s00373-015-1598-2

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  • DOI: https://doi.org/10.1007/s00373-015-1598-2

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