Almost self-complementary factors of complete bipartite graphs

AbstractA complete bipartite graph without one edge, K̃n,m, is called almost complete bipartite graph. A graph K̃2n+1,2m+1 that can be decomposed into two isomorphic factors with a given diameter d is called d-isodecomposable. We prove that K̃2n+1, 2m+1 is d-isodecomposable only if d = 3, 4, 5, 6 or ∞ and completely determine all d-isodecomposable almost complete bipartite graphs for each diameter. For d = ∞ we, moreover, present all classes of possible disconnected factors