On a classification of Hamiltonian tournaments

Marco Burzio; Davide Carlo Demaria

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Displaying similar documents to “On a classification of Hamiltonian tournaments”

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Ruskey and Savage asked the following question: Does every matching in a hypercube Qn for n ≥ 2 extend to a Hamiltonian cycle of Qn? Fink confirmed that every perfect matching can be extended to a Hamiltonian cycle of Qn, thus solved Kreweras’ conjecture. Also, Fink pointed out that every matching can be extended to a Hamiltonian cycle of Qn for n ∈ {2, 3, 4}. In this paper, we prove that every matching in Q5 can be extended to a Hamiltonian cycle of Q5.

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A nonempty vertex set X ⊆ V (G) of a hamiltonian graph G is called an H-force set of G if every X-cycle of G (i.e. a cycle of G containing all vertices of X) is hamiltonian. The H-force number h(G) of a graph G is defined to be the smallest cardinality of an H-force set of G. In the paper the study of this parameter is introduced and its value or a lower bound for outerplanar graphs, planar graphs, k-connected graphs and prisms over graphs is determined.

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We first show that if a graph G of order n contains a hamiltonian path connecting two nonadjacent vertices u and v such that d(u)+d(v) ≥ n, then G is pancyclic. By using this result, we prove that if G is hamiltonian with order n ≥ 20 and if G has two nonadjacent vertices u and v such that d(u)+d(v) ≥ n+z, where z = 0 when n is odd and z = 1 otherwise, then G contains a cycle of length m for each 3 ≤ m ≤ max (dC(u,v)+1, [(n+19)/13]), $d_{C} (u, v)$ being the distance of u and v on a hamiltonian cycle...

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Cycles with a given number of vertices from each partite set in regular multipartite tournaments

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If $x$ is a vertex of a digraph $D$ , then we denote by $d^{+} (x)$ and $d^{-} (x)$ the outdegree and the indegree of $x$ , respectively. A digraph $D$ is called regular, if there is a number $p \in ℕ$ such that $d^{+} (x) = d^{-} (x) = p$ for all vertices $x$ of $D$ . A $c$ -partite tournament is an orientation of a complete $c$ -partite graph. There are many results about directed cycles of a given length or of directed cycles with vertices from a given number of partite sets. The idea is now to combine the two properties. In this article, we examine in particular,...

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