Opuscula Math. 29, no. 4 (2009), 337-343

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.

Full text (pdf)

  • 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

Download this article's citation as:
a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.