On equitably 2‐colourable odd cycle decompositions

Abstract

AbstractAn ‐cycle decomposition of is said to be equitably 2‐colourable if there is a 2‐vertex‐colouring of such that each colour is represented (approximately) an equal number of times on each cycle: more precisely, we ask that in each cycle of the decomposition, each colour appears on or of the vertices of . In this paper we study the existence of equitably 2‐colourable ‐cycle decompositions of , where is odd, and prove the existence of such a decomposition for (mod ).