Work

Rainbow Even Cycles

Year: 2024

Type: article

Abstract: . We prove that every family of (not necessarily distinct) even cycles [Formula: see text] on some fixed [Formula: see text]-vertex set has a rainbow even cycle (that is, a set of edges from distinct [Formula: see text]’s, forming an even cycle). This resolves an open problem of Aharoni, Briggs, Holzman and Jiang. Moreover, the result is best possible for every positive integer [Formula: see text].

Source: SIAM Journal on Discrete Mathematics

DOI: 10.1137/23m1564808

Authors: Zichao Dong, Zijian Xu

Institutions: Carnegie Mellon University, Peking University

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Institute for Basic Science, H2020 European Research Council

Awards: From Geometry to Combinatorics and Back: Escaping the Curse of Dimensionality, Problems in Extremal and Geometric Combinatorics