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

Matchings Extend to Hamiltonian Cycles in 5-Cube

Fan Wang, Weisheng Zhao (2018)

Discussiones Mathematicae Graph Theory

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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.

On Vertices Enforcing a Hamiltonian Cycle

Igor Fabrici, Erhard Hexel, Stanislav Jendrol’ (2013)

Discussiones Mathematicae Graph Theory

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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.

Pancyclism and small cycles in graphs

Ralph Faudree, Odile Favaron, Evelyne Flandrin, Hao Li (1996)

Discussiones Mathematicae Graph Theory

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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...

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

Lutz Volkmann, Stefan Winzen (2006)

Czechoslovak Mathematical Journal

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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 ∈ 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,...