Graphs with Girth at Least 8 are b-continuous

被引:0
|
作者
Ibiapina, Allen [1 ]
Silva, Ana [1 ]
机构
[1] Univ Fed Ceara, Dept Matemat, Ctr Cincias, ParGO Grp Paralelism Graphs & Optimizat, Fortaleza, Ceara, Brazil
关键词
b-chromatic number; b-continuity; girth; bipartite graphs; CHROMATIC NUMBER;
D O I
10.1016/j.entcs.2019.08.059
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
A b-coloring of a graph is a proper coloring such that each color class has at least one vertex which is adjacent to each other color class. The b-spectrum of G is the set S-b(G) of integers k such that G has a b-coloring with k colors and b(G) = max S-b(G) is the b-chromatic number of G. A graph is b-continous if S-b(G) = [chi(G), b(G)] boolean AND Z. An infinite number of graphs that are not b-continuous is known. It is also known that graphs with girth at least 10 are b-continuous. In this work, we prove that graphs with girth at least 8 are b-continuous, and that the b-spectrum of a graph G with girth at least 7 contains the integers between 2 chi(G) and b(G). This generalizes a previous result by Linhares-Sales and Silva (2017), and tells that graphs with girth at least 7 are, in a way, almost b-continuous.
引用
收藏
页码:677 / 684
页数:8
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