Rainbow eulerian multidigraphs and the product of cycles

Abstract

An arc colored eulerian multidigraph with l colors is rainbow eulerian if there is an eulerian circuit in which a sequence of l colors repeats. The digraph product that refers the title was introduced by Figueroa-Centeno et al. as follows: let D be a digraph and let G be a family of digraphs such that V (F) = V for every F ¿ G