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
收藏
页码：138 / 151
页数：14
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