Properly colored cycles of different lengths in edge-colored complete graphs

Tingting Han, Shenggui Zhang, Yandong Bai

科研成果: 期刊稿件文章同行评审

摘要

A cycle in an edge-colored graph is called properly colored if all of its adjacent edges have distinct colors. Let Knc be an edge-colored complete graph with n vertices and let k be a positive integer. Denote by Δmon(Knc) the maximum number of edges of the same color incident with a vertex of Knc. In this paper, we show that (i) if Δmon(Knc)⩽n−2k, then Knc contains k properly colored cycles of different lengths and the bound is sharp; (ii) if Δmon(Knc)⩽n−2k+1−2k+4, then Knc contains k vertex-disjoint properly colored cycles of different lengths; in particular, Δmon(Knc)⩽n−6 suffices for the existence of two vertex-disjoint properly colored cycles of different lengths.

源语言英语
文章编号113653
期刊Discrete Mathematics
346
12
DOI
出版状态已出版 - 12月 2023

指纹

探究 'Properly colored cycles of different lengths in edge-colored complete graphs' 的科研主题。它们共同构成独一无二的指纹。

引用此