Hamiltonian cycles in 2-tough 2K2-free graphs

Katsuhiro Ota; Masahiro Sanka

doi:10.1002/jgt.22852

Hamiltonian cycles in 2-tough 2K₂-free graphs

Katsuhiro Ota, Masahiro Sanka

Department of Mathematics

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

1 Citation (Scopus)

Abstract

A graph (Formula presented.) is called a (Formula presented.) -free graph if it does not contain (Formula presented.) as an induced subgraph. In 2014, Broersma, Patel, and Pyatkin showed that every 25-tough (Formula presented.) -free graph on at least three vertices is Hamiltonian. Recently, Shan improved this result by showing that 3-tough is sufficient instead of 25-tough. In this paper, we show that every 2-tough (Formula presented.) -free graph on at least three vertices is Hamiltonian, which was conjectured by Gao and Pasechnik.

Original language	English
Pages (from-to)	769-781
Number of pages	13
Journal	Journal of Graph Theory
Volume	101
Issue number	4
DOIs	https://doi.org/10.1002/jgt.22852
Publication status	Published - 2022 Dec

Keywords

2-factor
2K-free graph
Hamiltonian cycle
toughness

ASJC Scopus subject areas

Geometry and Topology
Discrete Mathematics and Combinatorics

Access to Document

10.1002/jgt.22852

Cite this

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title = "Hamiltonian cycles in 2-tough 2K2-free graphs",

abstract = "A graph (Formula presented.) is called a (Formula presented.) -free graph if it does not contain (Formula presented.) as an induced subgraph. In 2014, Broersma, Patel, and Pyatkin showed that every 25-tough (Formula presented.) -free graph on at least three vertices is Hamiltonian. Recently, Shan improved this result by showing that 3-tough is sufficient instead of 25-tough. In this paper, we show that every 2-tough (Formula presented.) -free graph on at least three vertices is Hamiltonian, which was conjectured by Gao and Pasechnik.",

keywords = "2-factor, 2K-free graph, Hamiltonian cycle, toughness",

author = "Katsuhiro Ota and Masahiro Sanka",

note = "Funding Information: We would like to express our gratitude to the referees for their helpful comments. The first author's work (K. Ota) was supported by JSPS KAKENHI (Grant Number 16H03952). The second author's work (M. Sanka) was supported by JST Doctoral Program Student Support Project (Grant Number JPMJSP2123). Publisher Copyright: {\textcopyright} 2022 Wiley Periodicals LLC.",

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T1 - Hamiltonian cycles in 2-tough 2K2-free graphs

AU - Ota, Katsuhiro

AU - Sanka, Masahiro

N1 - Funding Information: We would like to express our gratitude to the referees for their helpful comments. The first author's work (K. Ota) was supported by JSPS KAKENHI (Grant Number 16H03952). The second author's work (M. Sanka) was supported by JST Doctoral Program Student Support Project (Grant Number JPMJSP2123). Publisher Copyright: © 2022 Wiley Periodicals LLC.

PY - 2022/12

Y1 - 2022/12

N2 - A graph (Formula presented.) is called a (Formula presented.) -free graph if it does not contain (Formula presented.) as an induced subgraph. In 2014, Broersma, Patel, and Pyatkin showed that every 25-tough (Formula presented.) -free graph on at least three vertices is Hamiltonian. Recently, Shan improved this result by showing that 3-tough is sufficient instead of 25-tough. In this paper, we show that every 2-tough (Formula presented.) -free graph on at least three vertices is Hamiltonian, which was conjectured by Gao and Pasechnik.

AB - A graph (Formula presented.) is called a (Formula presented.) -free graph if it does not contain (Formula presented.) as an induced subgraph. In 2014, Broersma, Patel, and Pyatkin showed that every 25-tough (Formula presented.) -free graph on at least three vertices is Hamiltonian. Recently, Shan improved this result by showing that 3-tough is sufficient instead of 25-tough. In this paper, we show that every 2-tough (Formula presented.) -free graph on at least three vertices is Hamiltonian, which was conjectured by Gao and Pasechnik.

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KW - 2K-free graph

KW - Hamiltonian cycle

KW - toughness

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