Work

Rainbow Odd Cycles

Year: 2021

Type: article

Abstract: We prove that every family of (not necessarily distinct) odd cycles $O_1, \dots, O_{2\lceil n/2 \rceil-1}$ 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.

Source: SIAM Journal on Discrete Mathematics

DOI: 10.1137/20m1380557

Authors: Ron Aharoni, Joseph Briggs, Ron Holzman, Zilin Jiang

Institutions: Technion – Israel Institute of Technology, Arizona State University

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green