Planar 4-critical graphs with four triangles

被引：13

作者：

Borodin, Oleg V. ^{[1
,2
]}

Dvorak, Zdenek ^{[3
]}

Kostochka, Alexandr V. ^{[1
,4
]}

Lidicky, Bernard ^{[4
]}

Yancey, Matthew ^{[4
]}

机构：

[1] Sobolev Inst Math, Novosibirsk 630090, Russia

[2] Novosibirsk State Univ, Novosibirsk 630090, Russia

[3] Charles Univ Prague, Inst Comp Sci, Prague, Czech Republic

[4] Univ Illinois, Urbana, IL 61801 USA

来源：

EUROPEAN JOURNAL OF COMBINATORICS | 2014年 / 41卷

基金：

美国国家科学基金会; 俄罗斯基础研究基金会;

关键词：

D O I：

10.1016/j.ejc.2014.03.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

By the Grunbaum-Aksenov Theorem (extending Grotzsch's Theorem) every planar graph with at most three triangles is 3-colorable. However, there are infinitely many planar 4-critical graphs with exactly four triangles. We describe all such graphs. This answers a question of Erdos from 1990. (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：138 / 151

页数：14

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