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

Mikio Kano, Shun ichi Maezawa, Katsuhiro Ota, Masao Tsugaki, Takamasa Yashima

Research output: Contribution to journalArticle

Abstract

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 |G|, 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.

Original languageEnglish
Article number112042
JournalDiscrete Mathematics
Volume343
Issue number11
DOIs
Publication statusPublished - 2020 Nov

Keywords

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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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