Degree conditions restricted to induced paths for hamiltonicity of claw-heavy graphs

Bin Long Li; Bo Ning; Sheng Gui Zhang

doi:10.1007/s10114-016-5735-5

Degree conditions restricted to induced paths for hamiltonicity of claw-heavy graphs

Bin Long Li
, Bo Ning
, Sheng Gui Zhang

School of Mathematics and Statistics

Northwestern Polytechnical University Xian
European Centre of Excellence NTIS
Tianjin University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Broersma and Veldman proved that every 2-connected claw-free and P₆-free graph is hamiltonian. Chen et al. extended this result by proving every 2-connected claw-heavy and P₆-free graph is hamiltonian. On the other hand, Li et al. constructed a class of 2-connected graphs which are claw-heavy and P₆-o-heavy but not hamiltonian. In this paper, we further give some Ore-type degree conditions restricting to induced copies of P₆ of a 2-connected claw-heavy graph that can guarantee the graph to be hamiltonian. This improves some previous related results.

Original language	English
Pages (from-to)	301-310
Number of pages	10
Journal	Acta Mathematica Sinica, English Series
Volume	33
Issue number	2
DOIs	https://doi.org/10.1007/s10114-016-5735-5
State	Published - 1 Feb 2017

Keywords

Hamiltonian graph
claw-heavy graph
closure theory
degree condition
forbidden subgraph condition

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10.1007/s10114-016-5735-5

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title = "Degree conditions restricted to induced paths for hamiltonicity of claw-heavy graphs",

abstract = "Broersma and Veldman proved that every 2-connected claw-free and P6-free graph is hamiltonian. Chen et al. extended this result by proving every 2-connected claw-heavy and P6-free graph is hamiltonian. On the other hand, Li et al. constructed a class of 2-connected graphs which are claw-heavy and P6-o-heavy but not hamiltonian. In this paper, we further give some Ore-type degree conditions restricting to induced copies of P6 of a 2-connected claw-heavy graph that can guarantee the graph to be hamiltonian. This improves some previous related results.",

keywords = "Hamiltonian graph, claw-heavy graph, closure theory, degree condition, forbidden subgraph condition",

author = "Li, \{Bin Long\} and Bo Ning and Zhang, \{Sheng Gui\}",

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T1 - Degree conditions restricted to induced paths for hamiltonicity of claw-heavy graphs

AU - Li, Bin Long

AU - Ning, Bo

AU - Zhang, Sheng Gui

PY - 2017/2/1

Y1 - 2017/2/1

N2 - Broersma and Veldman proved that every 2-connected claw-free and P6-free graph is hamiltonian. Chen et al. extended this result by proving every 2-connected claw-heavy and P6-free graph is hamiltonian. On the other hand, Li et al. constructed a class of 2-connected graphs which are claw-heavy and P6-o-heavy but not hamiltonian. In this paper, we further give some Ore-type degree conditions restricting to induced copies of P6 of a 2-connected claw-heavy graph that can guarantee the graph to be hamiltonian. This improves some previous related results.

AB - Broersma and Veldman proved that every 2-connected claw-free and P6-free graph is hamiltonian. Chen et al. extended this result by proving every 2-connected claw-heavy and P6-free graph is hamiltonian. On the other hand, Li et al. constructed a class of 2-connected graphs which are claw-heavy and P6-o-heavy but not hamiltonian. In this paper, we further give some Ore-type degree conditions restricting to induced copies of P6 of a 2-connected claw-heavy graph that can guarantee the graph to be hamiltonian. This improves some previous related results.

KW - Hamiltonian graph

KW - claw-heavy graph

KW - closure theory

KW - degree condition

KW - forbidden subgraph condition

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JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 2

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Degree conditions restricted to induced paths for hamiltonicity of claw-heavy graphs

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