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On Hamiltonicity of 3-Connected Claw-Free Graphs

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Abstract

Lai, Shao and Zhan (J Graph Theory 48:142–146, 2005) showed that every 3-connected N 2-locally connected claw-free graph is Hamiltonian. In this paper, we generalize this result and show that every 3-connected claw-free graph G such that every locally disconnected vertex lies on some induced cycle of length at least 4 with at most 4 edges contained in some triangle of G is Hamiltonian. It is best possible in some sense.

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Authors and Affiliations

  1. School of Mathematics, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China

    Runli Tian & Liming Xiong

  2. Department of Mathematics, Qinghai University for Nationalities, Xining, 810000, People’s Republic of China

    Liming Xiong

  3. School of Mathematical Sciences, Shanxi University, Taiyuan, 030006, People’s Republic of China

    Zhaohong Niu

Authors
  1. Runli Tian
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  2. Liming Xiong
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  3. Zhaohong Niu
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Correspondence to Liming Xiong.

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Tian, R., Xiong, L. & Niu, Z. On Hamiltonicity of 3-Connected Claw-Free Graphs. Graphs and Combinatorics 30, 1261–1269 (2014). https://doi.org/10.1007/s00373-013-1343-7

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  • DOI: https://doi.org/10.1007/s00373-013-1343-7

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