Color degree sum conditions for properly colored spanning trees in edge-colored graphs

被引：1

作者：

Kano, Mikio ^{[1
]}

Maezawa, Shun-ichi ^{[2
]}

Ota, Katsuhiro ^{[3
]}

Tsugaki, Masao ^{[4
]}

Yashima, Takamasa ^{[3
,5
]}

机构：

[1] Ibaraki Univ, Hitachi, Ibaraki, Japan

[2] Yokohama Natl Univ, Yokohama, Kanagawa, Japan

[3] Keio Univ, Yokohama, Kanagawa, Japan

[4] Tokyo Univ Sci, Tokyo, Japan

[5] Seikei Univ, Tokyo, Japan

来源：

DISCRETE MATHEMATICS | 2020年 / 343卷 / 11期

关键词：

Edge-colored graph; Spanning tree; Properly colored; Rainbow;

D O I：

10.1016/j.disc.2020.112042

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a vertex v of an edge-colored graph, the color degree of v is the number of colors appeared in edges incident with v. An edge-colored graph is called properly colored if no two adjacent edges have the same color. In this paper, we prove that if the minimum color degree sum of two adjacent vertices of an edge-colored connected graph G is at least vertical bar G vertical bar, then G has a properly colored spanning tree. This is a generalization of the result proved by Cheng, Kano and Wang. We also show the sharpness of this lower bound of the color degree sum. (C) 2020 Elsevier B.V. All rights reserved.

引用

页数：5

共 7 条

[1] Multicolored trees in complete graphs [J].