Self-complementary factors of almost complete tripartite graphs of even order

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A complete tripartite graph without one edge, K̃m1, m2, m3 is called almost complete tripartite graph. A graph K̃m1, m2, m3 that can be decomposed into two isomorphic factors with a given diameter d is called d-halvable. We prove that K̃m1, m2, m3 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.

Original languageEnglish (US)
Pages (from-to)111-122
Number of pages12
JournalDiscrete Mathematics
Issue number1-3
StatePublished - Jun 6 2001


  • Graph decompositions
  • Isomorphic factors
  • Self-complementary graphs


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