Rainbow odd cycles

Ron Aharoni, Joseph Briggs, Ron Holzman, Zilin Jiang

Abstract

We prove that every family of (not necessarily distinct) odd cycles O1, . . ., O2[n/2] - 1 in the complete graph Kn on n vertices has a rainbow odd cycle (that is, a set of edges from distinct Oi's, forming an odd cycle). As part of the proof, we characterize those families of n odd cycles in Kn+1 that do not have any rainbow odd cycle. We also characterize those families of n cycles in Kn+1, as well as those of n edge-disjoint nonempty subgraphs of Kn+1, without any rainbow cycle.

Original languageEnglish (US)
JournalSIAM Journal on Discrete Mathematics
Volume35
Issue number4
DOIs
StatePublished - 2021
Externally publishedYes

Keywords

  • Cactus graph
  • Odd cycle
  • Rado's theorem for matroids
  • Rainbow cycle

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint

Dive into the research topics of 'Rainbow odd cycles'. Together they form a unique fingerprint.

Cite this