Range of diameters of complementary factors of almost complete tripartite graphs

Abstract

A complete tripartite graph without one edge, K̃_m1,m2,m3, is called almost complete tripartite graph. A graph that K̃_m1,m2,m3 that can be decomposed into two isomorphic factors with a given diameter d is called d-halvable. We prove that K̃_m1,m2,m3 is d-halvable for a finite d only if d ≤ 5.