The b-Chromatic Number of Cubic Graphs

被引：41
|
作者：
Jakovac, Marko [1 ]
Klavzar, Sandi [1 ,2 ]
机构：
[1] Univ Maribor, Fac Nat Sci & Math, SLO-2000 Maribor, Slovenia
[2] Univ Ljubljana, Fac Math & Phys, Ljubljana 1000, Slovenia
来源：
GRAPHS AND COMBINATORICS | 2010年 / 26卷 / 01期
关键词：
Chromatic number; b-Chromatic number; Cubic graph; Petersen graph; BOUNDS;
D O I：
10.1007/s00373-010-0898-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The b-chromatic number of a graph G is the largest integer k such that G admits a proper k-coloring in which every color class contains at least one vertex adjacent to some vertex in all the other color classes. It is proved that with four exceptions, the b-chromatic number of cubic graphs is 4. The exceptions are the Petersen graph, K (3,3), the prism over K (3), and one more sporadic example on 10 vertices.
引用
收藏
页码：107 / 118
页数：12
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