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

Edge condition for hamiltonicity in balanced tripartite graphs


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.
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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ISSN 1232−9274, e-ISSN 2300−6919, DOI http://dx.doi.org/10.7494/OpMath
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