3-CHOOSABILITY OF TRIANGLE-FREE PLANAR GRAPHS WITH CONSTRAINTS ON 4-CYCLES

被引：7

作者：

Dvorak, Zdenek ^{[1
]}

Lidicky, Bernard ^{[1
]}

Skrekovski, Riste ^{[2
]}

机构：

[1] Charles Univ Prague, Fac Math & Phys, Dept Appl Math, Prague 11800, Czech Republic

[2] Univ Ljubljana, Dept Math, Ljubljana 1111, Slovenia

来源：

SIAM JOURNAL ON DISCRETE MATHEMATICS | 2010年 / 24卷 / 03期

关键词：

planar graph; triangle-free graph; coloring; list coloring; choosability; LIST COLORINGS; LEAST; 4; GIRTH; MAP;

D O I：

10.1137/080743020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A graph is k-choosable if it can be colored whenever every vertex has a list of at least k available colors. We prove that if a triangle-free planar graph is not 3-choosable, then it contains a 4-cycle that intersects another 4- or 5-cycle in exactly one edge. This strengthens Thomassen's result [C. Thomassen, J. Combin. Theory Ser. B, 64 (1995), pp. 101-107] that every planar graph of girth at least 5 is 3-choosable. In addition, this implies that every triangle-free planar graph without 6- and 7-cycles is 3-choosable.

引用

页码：934 / 945

页数：12

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