2-distance choice number of planar graphs with maximal degree no more than 4

被引：0
|
作者：
Zhou, Wenjuan [1 ]
Sun, Lei [1 ]
机构：
[1] Shandong Normal Univ, Sch Math & Stat, Jinan 250014, Peoples R China
来源：
DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS | 2021年 / 13卷 / 05期
基金：
中国国家自然科学基金;
关键词：
Planar graph; 2-distance k-choosable; girth; maximum degree;
D O I：
10.1142/S1793830921500518
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Regarding the 2-distance coloring of planar graphs, in 1977, Wegner conjectured that for a graph G: (1) chi(2)(G) <= 7 if Delta(G) = 3. (2) chi(2)(G) <= Delta(G) + 5 if 4 <= Delta(G) <= 7. (3) chi(2)(G) <= L left perpendicular3/2 Delta(G)right perpendicular + 1 if Delta(G) >= 8. In this paper, we proved that for every planar graph with maximum degree Delta(G) <= 4: (1) chi(l)(2)(G) <= 10 if g(G) >= 6. (2) chi(l)(2)(G) <= 7 if g(G) >= 10.
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页数：7
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