A complete bipartite graph without properly colored cycles of length four

被引：6

作者：

Cada, Roman ^{[1
,2
]}

Ozeki, Kenta ^{[3
]}

Yoshimoto, Kiyoshi ^{[4
]}

机构：

[1] Univ West Bohemia, NTIS, Dept Math, Plzen, Czech Republic

[2] Univ West Bohemia, CE ITI European Ctr Excellence, Plzen, Czech Republic

[3] Yokohama Natl Univ, Fac Environm & Informat Sci, Yokohama, Kanagawa, Japan

[4] Nihon Univ, Coll Sci & Technol, Dept Math, Tokyo, Japan

来源：

JOURNAL OF GRAPH THEORY | 2020年 / 93卷 / 02期

关键词：

complete bipartite graph; minimum color degree; properly colored cycle; ANTI-RAMSEY NUMBERS;

D O I：

10.1002/jgt.22480

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A subgraph of an edge-colored graph is said to be properly colored, or shortly PC, if any two adjacent edges have different colors. Fujita, Li, and Zhang gave a decomposition theorem for edge-colorings of complete bipartite graphs without PC C4. However, their decomposition just focuses on a local structure. In this paper, we give a new and global decomposition theorem for edge-colorings of complete bipartite graphs without PC C4. Our decomposition gives a corollary on the existence of a monochromatic star with almost sharp bound.

引用

页码：168 / 180

页数：13

共 16 条

[1] Cycles and Paths in Edge-Colored Graphs with Given Degrees [J].