RAINBOW EVEN CYCLES.

We prove that every family of (not necessarily distinct) even cycles D₁,...D⌊_1.2(n-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. [ABSTRACT FROM AUTHOR]