Counterexamples to Thomassen’s Conjecture on Decomposition of Cubic Graphs

Thomas Bellitto; Tereza Klimošová; Martin Merker; Marcin Witkowski; Yelena Yuditsky

doi:10.1007/s00373-021-02380-z

Counterexamples to Thomassen’s Conjecture on Decomposition of Cubic Graphs

Thomas Bellitto, Tereza Klimošová, Martin Merker, Marcin Witkowski, Yelena Yuditsky

Department of Computer Science

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

1 Scopus citations

Abstract

We construct an infinite family of counterexamples to Thomassen’s conjecture that the vertices of every 3-connected, cubic graph on at least 8 vertices can be colored blue and red such that the blue subgraph has maximum degree at most 1 and the red subgraph minimum degree at least 1 and contains no path on 4 vertices.

Original language	English
Pages (from-to)	2595-2599
Number of pages	5
Journal	Graphs and Combinatorics
Volume	37
Issue number	6
DOIs	https://doi.org/10.1007/s00373-021-02380-z
State	Published - 1 Nov 2021

Keywords

Cubic graphs
Graph decomposition
Thomassen’s conjecture

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1007/s00373-021-02380-z

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abstract = "We construct an infinite family of counterexamples to Thomassen{\textquoteright}s conjecture that the vertices of every 3-connected, cubic graph on at least 8 vertices can be colored blue and red such that the blue subgraph has maximum degree at most 1 and the red subgraph minimum degree at least 1 and contains no path on 4 vertices.",

keywords = "Cubic graphs, Graph decomposition, Thomassen{\textquoteright}s conjecture",

author = "Thomas Bellitto and Tereza Klimo{\v s}ov{\'a} and Martin Merker and Marcin Witkowski and Yelena Yuditsky",

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AU - Klimošová, Tereza

AU - Merker, Martin

AU - Witkowski, Marcin

AU - Yuditsky, Yelena

PY - 2021/11/1

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N2 - We construct an infinite family of counterexamples to Thomassen’s conjecture that the vertices of every 3-connected, cubic graph on at least 8 vertices can be colored blue and red such that the blue subgraph has maximum degree at most 1 and the red subgraph minimum degree at least 1 and contains no path on 4 vertices.

AB - We construct an infinite family of counterexamples to Thomassen’s conjecture that the vertices of every 3-connected, cubic graph on at least 8 vertices can be colored blue and red such that the blue subgraph has maximum degree at most 1 and the red subgraph minimum degree at least 1 and contains no path on 4 vertices.

KW - Cubic graphs

KW - Graph decomposition

KW - Thomassen’s conjecture

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ER -

Counterexamples to Thomassen’s Conjecture on Decomposition of Cubic Graphs

Abstract

Keywords

ASJC Scopus subject areas

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