Counterexamples to Thomassen's Conjecture on Decomposition of Cubic Graphs

被引：1

作者：

Bellitto, Thomas ^{[1
]}

Klimosova, Tereza ^{[2
]}

Merker, Martin ^{[3
]}

Witkowski, Marcin ^{[4
]}

Yuditsky, Yelena ^{[5
]}

机构：

[1] Univ Southern Denmark, Dept Math & Comp Sci, Odense, Denmark

[2] Charles Univ Prague, Dept Appl Math, Fac Math & Phys, Prague, Czech Republic

[3] Tech Univ Denmark, Dept Appl Math & Comp Sci, Lyngby, Denmark

[4] Adam Mickiewicz Univ, Fac Math & Comp Sci, Poznan, Poland

[5] Ben Gurion Univ Negev, Dept Math, Beer Sheva, Israel

来源：

GRAPHS AND COMBINATORICS | 2021年 / 37卷 / 06期

基金：

欧洲研究理事会;

关键词：

Cubic graphs; Thomassen's conjecture; Graph decomposition;

D O I：

10.1007/s00373-021-02380-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：2595 / 2599

页数：5

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