Tripartite graphs with given degree set

Abstract

If k ≥ 1, then the global degree set of a k-partite graph G = ( V 1 , V 2 , . . . , V k , E ) is the set of the distinct degrees of the vertices of G , while if k ≥ 2, then the distributed degree set of G is the family of the k degree sets of the vertices of the parts of G . We propose algorithms to construct bipartite and tripartite graphs with prescribed global and distributed degree sets consisting from arbitrary nonnegative integers. We also present a review of the similar known results on digraphs.