Maximal sets of Hamilton cycles in [formula omitted

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 λ2n⌊r+34⌋≤t≤min{⌊λ2n2(r−1)2⌋,⌊λ1(n−1)+λ2n(r−1)2⌋}, the upper bound being best possible. The results proved make use of the method of amalgamations.