A note on the shortness coefficient and the hamiltonicity of 4-connected line graphs

Liming Xiong; Roman Kužel

doi:10.1007/s00373-004-0595-7

A note on the shortness coefficient and the hamiltonicity of 4-connected line graphs

Liming Xiong^*
, Roman Kužel

^*Corresponding author for this work

School of Mathematics and Statistics

Jiangxi Normal University
University of West Bohemia
Charles University

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

Abstract

Thomassen proposed a well-known conjecture: every 4-connected line graph is hamiltonian. In this note, we show that Thomassen's conjecture is equivalent to the statement that the shortness coefficient of the class of all 4-connected line graphs is one and the statement that the shortness coefficient of the class of all 4-connected claw-free graphs is one respectively.

Original language	English
Pages (from-to)	137-144
Number of pages	8
Journal	Graphs and Combinatorics
Volume	21
Issue number	1
DOIs	https://doi.org/10.1007/s00373-004-0595-7
Publication status	Published - Mar 2005

Keywords

Dominating cycle conjecture
Essentially edge connected graph
Line graph
Shortness coefficient
Thomassen's conjecture

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Cite this

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title = "A note on the shortness coefficient and the hamiltonicity of 4-connected line graphs",

abstract = "Thomassen proposed a well-known conjecture: every 4-connected line graph is hamiltonian. In this note, we show that Thomassen's conjecture is equivalent to the statement that the shortness coefficient of the class of all 4-connected line graphs is one and the statement that the shortness coefficient of the class of all 4-connected claw-free graphs is one respectively.",

keywords = "Dominating cycle conjecture, Essentially edge connected graph, Line graph, Shortness coefficient, Thomassen's conjecture",

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AB - Thomassen proposed a well-known conjecture: every 4-connected line graph is hamiltonian. In this note, we show that Thomassen's conjecture is equivalent to the statement that the shortness coefficient of the class of all 4-connected line graphs is one and the statement that the shortness coefficient of the class of all 4-connected claw-free graphs is one respectively.

KW - Dominating cycle conjecture

KW - Essentially edge connected graph

KW - Line graph

KW - Shortness coefficient

KW - Thomassen's conjecture

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A note on the shortness coefficient and the hamiltonicity of 4-connected line graphs

Abstract

Keywords

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