On Hamiltonicity of 3-Connected Claw-Free Graphs

Runli Tian; Liming Xiong; Zhaohong Niu

doi:10.1007/s00373-013-1343-7

On Hamiltonicity of 3-Connected Claw-Free Graphs

Runli Tian
, Liming Xiong^*
, Zhaohong Niu

^*此作品的通讯作者

数学学院

Beijing Institute of Technology
Qinghai University
Shanxi University

科研成果: 期刊稿件 › 文章 › 同行评审

2 引用（Scopus）

摘要

Lai, Shao and Zhan (J Graph Theory 48:142-146, 2005) showed that every 3-connected N₂-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.

源语言	英语
页（从-至）	1261-1269
页数	9
期刊	Graphs and Combinatorics
卷	30
期	5
DOI	https://doi.org/10.1007/s00373-013-1343-7
出版状态	已出版 - 9月 2014

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abstract = "Lai, Shao and Zhan (J Graph Theory 48:142-146, 2005) showed that every 3-connected N2-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.",

keywords = "Claw-free graph, Hamiltonicity, Locally disconnected vertex, Singular edge, Singular k-cycle (property)",

author = "Runli Tian and Liming Xiong and Zhaohong Niu",

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AU - Xiong, Liming

AU - Niu, Zhaohong

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N2 - Lai, Shao and Zhan (J Graph Theory 48:142-146, 2005) showed that every 3-connected N2-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.

AB - Lai, Shao and Zhan (J Graph Theory 48:142-146, 2005) showed that every 3-connected N2-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.

KW - Claw-free graph

KW - Hamiltonicity

KW - Locally disconnected vertex

KW - Singular edge

KW - Singular k-cycle (property)

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ER -

On Hamiltonicity of 3-Connected Claw-Free Graphs

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