Self-complementary factors of almost complete tripartite graphs of even order

AbstractA complete tripartite graph without one edge, K̃m1,m2,m3, is called almost complete tripartite graph. A graph K̃m1,m2,m3 that can be decomposed into two isomorphic factors with a given diameter d is called d-halvable. We prove that K̃m1,m2,m3 is d-halvable for a finite d only if d⩽5 and completely determine all triples 2m′1+1,2m2′+1,2m3′ for which there exist d-halvable almost complete tripartite graphs for diameters 3,4 and 5, respectively