Rainbow odd cycles

Ron Aharoni; Joseph Briggs; Ron Holzman; Zilin Jiang

doi:10.1137/20M1380557

Rainbow odd cycles

Ron Aharoni, Joseph Briggs, Ron Holzman, Zilin Jiang

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We prove that every family of (not necessarily distinct) odd cycles O₁, . . ., O_2[n/2] - 1 in the complete graph K_n on n vertices has a rainbow odd cycle (that is, a set of edges from distinct O_i's, forming an odd cycle). As part of the proof, we characterize those families of n odd cycles in K_n+1 that do not have any rainbow odd cycle. We also characterize those families of n cycles in K_n+1, as well as those of n edge-disjoint nonempty subgraphs of K_n+1, without any rainbow cycle.

Original language	English (US)
Journal	SIAM Journal on Discrete Mathematics
Volume	35
Issue number	4
DOIs	https://doi.org/10.1137/20M1380557
State	Published - 2021

Keywords

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

ASJC Scopus subject areas

General Mathematics

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10.1137/20M1380557

Cite this

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title = "Rainbow odd cycles",

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.",

keywords = "Cactus graph, Odd cycle, Rado's theorem for matroids, Rainbow cycle",

author = "Ron Aharoni and Joseph Briggs and Ron Holzman and Zilin Jiang",

note = "Publisher Copyright: {\textcopyright} 2021 Society for Industrial and Applied Mathematics",

year = "2021",

doi = "10.1137/20M1380557",

language = "English (US)",

volume = "35",

journal = "SIAM Journal on Discrete Mathematics",

issn = "0895-4801",

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TY - JOUR

T1 - Rainbow odd cycles

AU - Aharoni, Ron

AU - Briggs, Joseph

AU - Holzman, Ron

AU - Jiang, Zilin

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - Cactus graph

KW - Odd cycle

KW - Rado's theorem for matroids

KW - Rainbow cycle

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DO - 10.1137/20M1380557

M3 - Article

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SN - 0895-4801

VL - 35

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

IS - 4

ER -

Rainbow odd cycles

Abstract

Keywords

ASJC Scopus subject areas

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