Borodin-Kostochka's conjecture on (P5, C4)-free graphs

被引：0
|
作者：
Gupta, Uttam K. [1 ]
Pradhan, D. [1 ]
机构：
[1] Indian Inst Technol ISM, Dept Math & Comp, Dhanbad, Bihar, India
来源：
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING | 2021年 / 65卷 / 1-2期
关键词：
Coloring; Chromatic bound; Borodin-Kostochka's conjecture; (P-5; C-4)-free graphs; CHROMATIC NUMBER; DELTA; CHI;
D O I：
10.1007/s12190-020-01419-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Brooks' theorem states that for a graph G, if Delta(G) >= 3, then chi(G) <= max{Delta(G),omega(G)}. Borodin and Kostochka conjectured a result strengthening Brooks' theorem, stated as, if Delta (G) >= 9, then chi (G) <= max {Delta(G)-1,omega(G)}. This conjecture is still open for general graphs. In this paper, we show that the conjecture is true for graphs having no induced path on five vertices and no induced cycle on four vertices.
引用
收藏
页码：877 / 884
页数：8
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