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

An almost complete tripartite graph image is obtained by removing an edge from the complete tripartite graph image. 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.