Edge-colorings of Km,n which forbid multicolored cycles

Hung-Lin Fu, Yuan Hsun Lo, Ryo Yu Pei

Research output: Contribution to journalArticlepeer-review

Abstract

A subgraph in an edge-colored graph is multicolored if all its edges receive distinct colors. In this paper,we study the proper edgecolorings of the complete bipartite graph Km,n which forbid multicolored cycles. Mainly,we prove that(1)for any integer k ≥ 2, if n ≥ 5k - 6, then any properly n-edge-colored Kk,n contains a multicolored C 2k,and(2)determine the order of the properly edge-colored complete bipartite graphs which forbid multicolored C6.

Original languageEnglish
Pages (from-to)77-84
Number of pages8
JournalUtilitas Mathematica
Volume90
StatePublished - 1 Mar 2013

Keywords

  • Complete bipartite graph
  • Edge-coloring
  • Multicolored cycle

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