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Browsing by Subject "tripartite graph"

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    Item type:Article, Access status: Open Access ,
    Edge condition for hamiltonicity in balanced tripartite graphs
    (2009) Adamus, Janusz
    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.