Coloring the square of maximal planar graphs with diameter two

被引：0
|
作者：
Wang, Yiqiao [1 ]
Huo, Jingjing [2 ]
Kong, Jiangxu [3 ]
Tan, Qiuyue [4 ]
机构：
[1] Beijing Univ Technol, Fac Sci, Beijing 100124, Peoples R China
[2] Hebei Univ Engn, Dept Math, Handan 056038, Peoples R China
[3] Hangzhou Normal Univ, Sch Math, Hangzhou 311121, Peoples R China
[4] Wuyi Univ, Dept Math & Comp, Wuyishan 354300, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2023年 / 459卷
关键词：
Wegner's conjecture; Chromatic number; Maximal planar graph; Diameter; 4-CYCLES; GIRTH;
D O I：
10.1016/j.amc.2023.128263
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let G be a maximal planar graph with diameter two and maximum degree Delta. Let chi (G2) denote the chromatic number of the square of... In this paper, we prove that chi(G2) = Delta + 1 if 2 <= Delta <= 3; chi(G(2)) <= 6 if Delta = 4; chi(G(2)) = 9 if Delta + 5; chi(G2) <=+ 5 if 6 <= Delta <= 7; and chi(G2) <= 3 Delta/2 + 1 if >= 8. All bounds are tight. This confirms the Wegner's conjecture for maximal planar graphs with diameter two.
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页数：10
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