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- W2785202364 abstract "In 2009, Adamus showed that if $G$ is a balanced tripartite graph of order $3n$, $n geq 2$, with at least $3n^2 - 2n + 2$ edges, then $G$ is hamiltonian and, in fact, $G$ is pancyclic. Removing all but one edge incident with any vertex of the complete, balanced tripartite graph $K(n,n,n)$ shows that this result is best possible. Here we extend the result to balanced $k$-partite graphs of order $kn$. We prove that for all integers $kgeq 3$ and $ngeq 1$, every balanced $k$-partite graph with $kn$ vertices and at least ${{(k^2-k)n^2-2n(k-1)+4}over 2}$ edges is pancyclic. We also prove a similar result for $k$-partite graphs that are not balanced." @default.
- W2785202364 created "2018-02-02" @default.
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- W2785202364 date "2018-01-24" @default.
- W2785202364 modified "2023-09-27" @default.
- W2785202364 title "A note on pancyclicity of $k$-partite graphs" @default.
- W2785202364 hasPublicationYear "2018" @default.
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