Decomposition of almost complete tripartite graphs into two isomorphic factors of fixed diameter

Abstract: An almost complete tripartite graph is obtained by removing an edge from the complete tripartite graph . A graph that can be decomposed into two isomorphic factors of diameter d is d-halvable. Fronček classified all 4-halvable almost complete tripartite graphs of even order in which the missing edge has its endpoints in two partite sets of odd order. In this paper, we classify 4-halvable almost complete tripartite graphs of even order for which the missing edge has an endpoint in a partite set with an even number of vertices. We also classify all 4-halvable almost complete tripartite graphs of odd order. Finally, we give a partial classification of 3- and 5-halvable almost complete tripartite graphs. [Copyright &y& Elsevier]