On the number of edge-disjoint one factors and the existence of k-factors in complete multipartite graphs Original Research Article

In this paper we use Tutteʹs f-factor theorem and the method of amalgamations to find necessary and sufficient conditions for the existence of a k-factor in the complete multipartite graph K(p(1), …, p(n)), conditions that are reminiscent of the Erdös-Gallai conditions for the existence of simple graphs with a given degree sequence. We then use this result to investigate the maximum number of edge-disjoint 1-factors in K(p(1), …, p(n)), settling the problem in the case where this number is greater than δ - p(2), where p(1) ⩽ p(2) ⩽…⩽ p(n).