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IMADA -Department of Mathematics and Computer Science |
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A vertex (an arc, respectively) of a digraph $D$ is called pancyclic, if it lies on a cycle of length $t$ for all $t\in\{3,\ldots,|V(D)|\}$. Moon ($\textit{On subtournaments of a tournament}$. Canad. Math. Bull. ${\bf 9}$, 1966) proved that every strong tournament is vertex-pancyclic and Alspach ($\textit{On Cycles of each length in regular tournaments}$. Canad. Math. Bull. ${\bf 10}$, 1967) confirmed that every regular tournament is arc-pancyclic. Since multipartite tournaments don't have the same vertex- and arc-pancyclicities as tournamnets, we have tried to extend the classical cycle concept to multipartite tournaments in various ways. In this talk, we will give an overview of quasi$_{\,\operatorname{x}}$-pancyclicities, $x\in\{\mbox{p, l, o, nl, ps}\}$, and pandashcyclicity in multipartite tournaments and leave a few open problems on this topic. Host: Jørgen Bang-Jensen SDU HOME | IMADA HOME Daniel Merkle |