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

共 50 条

[21] Counterexamples to Hedetniemi's conjecture
Shitov, Yaroslav
ANNALS OF MATHEMATICS, 2019, 190 (02) : 663 - 667
[22] Counterexamples to Mercat’s conjecture
Akash Kumar Sengupta
Archiv der Mathematik, 2016, 106 : 439 - 444
[23] Counterexamples to Knaster's conjecture
Chen, W
TOPOLOGY, 1998, 37 (02) : 401 - 405
[24] Connectivities for k-knitted graphs and for minimal counterexamples to Hadwiger's Conjecture
Kawarabayashi, Ken-ichi
Yu, Gexin
JOURNAL OF COMBINATORIAL THEORY SERIES B, 2013, 103 (03) : 320 - 326
[25] Counterexamples to the conjecture on orientations of graphs with minimum Wiener index
Fang, Yibin
Gao, Yubin
DISCRETE APPLIED MATHEMATICS, 2017, 232 : 213 - 220
[26] Counterexamples to a Conjecture on Wiener Index of Common Neighborhood Graphs
da Fonseca, Carlos M.
Ghebleh, Mohammad
Kanso, Ali
Stevanovic, Dragan
MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, 2014, 72 (01) : 333 - 338
[27] SEEKING COUNTEREXAMPLES TO THE RECONSTRUCTION CONJECTURE FOR GRAPHS - A RESEARCH NOTE
CVETKOVIC, D
ROWLINSON, P
GRAPH THEORY, 1989, : 52 - 62
[28] Counterexamples to the nonorientable genus conjecture for complete tripartite graphs
Ellingham, MN
Stephens, C
Zha, XY
EUROPEAN JOURNAL OF COMBINATORICS, 2005, 26 (3-4) : 387 - 399
[29] On a conjecture of Thomassen and Toft
Kriesell, M
JOURNAL OF GRAPH THEORY, 1999, 32 (02) : 118 - 122
[30] Contractible subgraphs, Thomassen's conjecture and the dominating cycle conjecture for snarks
Broersma, Hajo
Fijavz, Gasper
Kaiser, Tomas
Kuzel, Roman
Ryjacek, Zdenek
Vrana, Petr
DISCRETE MATHEMATICS, 2008, 308 (24) : 6064 - 6077

← 1 2 3 4 5 →