Approximate multipartite version of the Hajnal-Szemerédi theorem
Source:
21st Cumberland Conference on Graph Theory, Combinatorics, and Computing (2008)
Abstract:
Let q be a positve integer, and G be a q-partite simple graph on qn vertices, with n vertices in each vertex class. Let d = k/(k+1), where k=q+O(logq). If each vertex of G is adjacent to at least dn vertices in each of the other vertex classes, q is bounded and n is large enough, then G has a Kq-factor.
