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

School of Mathematics and Statistics

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

1 Scopus citations

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
State	Published - Jan 2020

Keywords

Claw-free
Dominating set
Hamiltonian property
Implicit claw-heavy

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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 - Broersma, Hajo

AU - Wang, Ligong

AU - Zhang, Shenggui

PY - 2020/1

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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

KW - Dominating set

KW - Hamiltonian property

KW - Implicit claw-heavy

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JO - Discrete Mathematics

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ER -

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

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Keywords

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