Conditions on subgraphs, degrees, and domination for hamiltonian properties of graphs

Wei  Zheng; Hajo Broersma; Ligong Wang; Shenggui Zhang

doi:10.1016/j.disc.2019.111644

Conditions on subgraphs, degrees, and domination for hamiltonian properties of graphs

Wei Zheng
, Hajo Broersma
, Ligong Wang^*
, Shenggui Zhang

^*Corresponding author for this work

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

2 Citations (Scopus)

123 Downloads (Pure)

Abstract

Motivated by a hamiltonicity result due to Ageev, involving claw-free graphs with a small domination number, we study analogous conditions that guarantee different types of hamiltonian properties. In our first main result we relax the condition on claw-freeness and obtain a common generalization of the result of Ageev and a recent result due to Cai. Our other results deal with similar conditions that guarantee traceability, pancyclicity and hamiltonian-connectivity. We also leave some open problems.

Original language	English
Article number	111644
Journal	Discrete mathematics
Volume	343
Issue number	1
DOIs	https://doi.org/10.1016/j.disc.2019.111644
Publication status	Published - Jan 2020

Keywords

Claw-free graph
Implicit claw-heavy
Dominating set
Hamiltonian property
22/2 OA procedure

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10.1016/j.disc.2019.111644

ArticleFinal published version, 338 KBLicence: Taverne

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title = "Conditions on subgraphs, degrees, and domination for hamiltonian properties of graphs",

abstract = "Motivated by a hamiltonicity result due to Ageev, involving claw-free graphs with a small domination number, we study analogous conditions that guarantee different types of hamiltonian properties. In our first main result we relax the condition on claw-freeness and obtain a common generalization of the result of Ageev and a recent result due to Cai. Our other results deal with similar conditions that guarantee traceability, pancyclicity and hamiltonian-connectivity. We also leave some open problems.",

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AU - Wang, Ligong

AU - Zhang, Shenggui

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Y1 - 2020/1

N2 - Motivated by a hamiltonicity result due to Ageev, involving claw-free graphs with a small domination number, we study analogous conditions that guarantee different types of hamiltonian properties. In our first main result we relax the condition on claw-freeness and obtain a common generalization of the result of Ageev and a recent result due to Cai. Our other results deal with similar conditions that guarantee traceability, pancyclicity and hamiltonian-connectivity. We also leave some open problems.

AB - Motivated by a hamiltonicity result due to Ageev, involving claw-free graphs with a small domination number, we study analogous conditions that guarantee different types of hamiltonian properties. In our first main result we relax the condition on claw-freeness and obtain a common generalization of the result of Ageev and a recent result due to Cai. Our other results deal with similar conditions that guarantee traceability, pancyclicity and hamiltonian-connectivity. We also leave some open problems.

KW - Claw-free graph

KW - Implicit claw-heavy

KW - Dominating set

KW - Hamiltonian property

KW - 22/2 OA procedure

U2 - 10.1016/j.disc.2019.111644

DO - 10.1016/j.disc.2019.111644

M3 - Article

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VL - 343

JO - Discrete mathematics

JF - Discrete mathematics

IS - 1

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ER -

Conditions on subgraphs, degrees, and domination for hamiltonian properties of graphs

Abstract

Keywords

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