Opuscula Math. 29, no. 4 (2009), 337-343
http://dx.doi.org/10.7494/OpMath.2009.29.4.337

 
Opuscula Mathematica

Edge condition for hamiltonicity in balanced tripartite graphs

Janusz Adamus

Abstract. A well-known theorem of Entringer and Schmeichel asserts that a balanced bipartite graph of order \(2n\) obtained from the complete balanced bipartite \(K_{n,n}\) by removing at most \(n-2\) edges, is bipancyclic. We prove an analogous result for balanced tripartite graphs: If \(G\) is a balanced tripartite graph of order \(3n\) and size at least \(3n^2-2n+2\), then \(G\) contains cycles of all lengths.

Keywords: Hamilton cycle, pancyclicity, tripartite graph, edge condition.

Mathematics Subject Classification: 05C38, 05C35.

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  • Janusz Adamus
  • The University of Western Ontario, Department of Mathematics, London, Ontario N6A 5B7 Canada
  • Jagiellonian University, Institute of Mathematics, ul. Łojasiewicza 6, 30-348 Kraków, Poland
  • Received: 2008-09-07.
  • Revised: 2009-07-20.
  • Accepted: 2009-08-02.
Opuscula Mathematica - cover

Cite this article as:
Janusz Adamus, Edge condition for hamiltonicity in balanced tripartite graphs, Opuscula Math. 29, no. 4 (2009), 337-343, http://dx.doi.org/10.7494/OpMath.2009.29.4.337

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