Pancyclic orderings of in-tournaments |
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Authors: | Meike Tewes |
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Affiliation: | Institut für Theoretische Mathematik, TU Bergakademie Freiberg, 09596, Freiberg, Germany |
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Abstract: | An in-tournament is an oriented graph such that the negative neighborhood of every vertex induces a tournament. In this paper, pancyclic orderings of a strong in-tournament D are investigated. This is a labeling, say x1,x2,…,xn, of the vertex set of D such that D[{x1,x2,…,xt}] is Hamiltonian for t=3,4,…,n. Moreover, we consider the related problem on weak pancyclic orderings, where the same holds for t4 and x1 belongs to an arbitrary oriented 3-cycle. We present sharp lower bounds for the minimum indegree ensuring the existence of a pancyclic or a weak pancyclic ordering in strong in-tournaments. |
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