.We prove that every family of (not necessarily distinct) even cycles \(D_1, , D1.2(n-1) +1\) on some fixed \(n\)-vertex set has a rainbow even cycle (that is, a set of edges from distinct \(D_i\)'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 \(n\).
No takes yet. Share an insight, caveat, or question.
Dong et al. (2024) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: