Rainbow Even Cycles

. We prove that every family of (not necessarily distinct) even cycles \ (D₁, , D ₁. ₂ (₍-₁) +₁\) on some fixed \ (n\) -vertex set has a rainbow even cycle (that is, a set of edges from distinct \ (Dᵢ\) '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\). Keywordseven cyclerainbow extremal graph theoryFrankenstein graphMSC codes05C3505C38