Maximal sets of Hamilton cycles in Kn^r;λ<inf>1</inf>,λ<inf>2</inf>

Abstract

Let Knr;λ1,λ2 be the r-partite multigraph in which each part has size n, where two vertices in the same part or different parts are joined by exactly λ1 edges or λ2 edges, respectively. It is proved that there exists a maximal set of t edge-disjoint Hamilton cycles in Knr;λ1,λ2 for [Formula presented], the upper bound being best possible. The results proved make use of the method of amalgamations.