Abstract
An almost complete tripartite graph K ˜ m 1 , m 2 , m 3 is obtained by removing an edge from the complete tripartite graph K m 1 , m 2 , m 3 . 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.
Published Version
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