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