On the vertex-pancyclicity of hypertournaments

Li, Hongwei; Li, Shengjia; Guo, Yubao; Surmacs, Michel

doi:10.1016/j.dam.2013.05.036

Cited by 15 publications

(8 citation statements)

References 4 publications

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“…D N + (v) ) is a tournament. Moon (1966) proved that every strong tournament is vertex-pancyclic; similar results on generalizations of tournaments where obtained by Bang-Jensen and Gutin (2009) and by Li et al (2013), where they proved, respectively, that every strong semicomplete digraph is vertex-pancyclic and that every khypertournament on n vertices, where 3 ≤ k ≤ n − 2, is vertex-pancyclic. Bang-Jensen and Huang (1995) characterized pancyclic and vertex-pancyclic quasi-transitive digraphs and Bang-Jensen et al (1997) characterized pancyclic and vertex-pancyclic locally semicomplete digraphs.…”

Section: Introductionsupporting

confidence: 56%

Vertex-pancyclism in the generalized sum of digraphs

Cordero‐Michel

Galeana‐Sánchez

2021

Discrete Applied Mathematics

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A digraph D = (V, A) of order n ≥ 3 is pancyclic, whenever D contains a directed cycle of length k for each k ∈ {3, . . . , n}; and D is vertex-pancyclic iff, for each vertex v ∈ V and each k ∈ {3, . . . , n}, D contains a directed cycle of length k passing through v.Let D1, D2, . . . , D k be a collection of pairwise vertex disjoint digraphs. The generalized sum (g.s.) of D1, D2, . . . ,. . , k; and (iii) for each pair of vertices belonging to different summands of D, there is exactly one arc between them, with an arbitrary but fixed direction. A digraph D in ⊕ k i=1 Di will be called a generalized sum (g.s.) of D1, D2, . . . , D k .In this paper we prove that if D1 and D2 are two vertex disjoint Hamiltonian digraphs and D ∈ D1⊕D2 is strong, then at least one of the following assertions holds: D is vertex-pancyclic, it is pancyclic or it is Hamiltonian and contains a directed cycle of length l for each l ∈ {3, . . . , max{|V (Di)| + 1 : i ∈ {1, 2}}}. Moreover, we prove that if D1, D2, . . . , D k is a collection of pairwise vertex disjoint Hamiltonian digraphs, ni = |V (Di)| for each i ∈ {1, . . . , k} and D ∈ ⊕ k i=1 Di is strong, then at least one of the following assertions holds: D is vertex-pancyclic, it is pancyclic or it is Hamiltonian and contains a directed cycle of length l for each l ∈ {3, . . . , max{ i∈S ni + 1 : S ⊂ {1, . . . , k} with |S| = k − 1}}.

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Section: Introductionsupporting

confidence: 56%

Vertex-pancyclism in the generalized sum of digraphs

Cordero‐Michel

Galeana‐Sánchez

2021

Discrete Applied Mathematics

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“…In 2006, some sufficient conditions for a hypertournament to be vertex-pancyclic were given by Petrovic and Thomassen [15], which were improved upon by Yang [22], in 2009. Finally, Gutin and Yeo's question was answered in the affirmative by Li et al [13], in 2013. Theorem 1.4 [13].…”

Section: Introduction and Terminologymentioning

confidence: 96%

“…Finally, Gutin and Yeo's question was answered in the affirmative by Li et al. , in 2013. Theorem Every strong k ‐hypertournament with n vertices, where

3 \leq k \leq n - 2

, is vertex‐pancyclic.…”

Section: Introduction and Terminologymentioning

confidence: 97%

Regular Hypertournaments and Arc‐Pancyclicity

Surmacs

2016

Journal of Graph Theory

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Abstract:A k-hypertournament H on n vertices (2 ≤ k ≤ n) is a pair H = (V, A), where V is the vertex set of H and A is a set of k-tuples of vertices, called arcs, such that for all subsets S ⊆ V with |S| = k, A contains exactly one permutation of S as an arc. Recently, Li et al. showed that any strong k-hypertournament H on n vertices, where 3 ≤ k ≤ n − 2, is vertexpancyclic, an extension of Moon's theorem for tournaments. In this article, we examine several generalizations of regular tournaments and prove the following generalization of Alspach's theorem concerning arc-pancyclicity: Every -regular k-hypertournament on n vertices, where 2 ≤ k ≤ n − 2, is arc-pancyclic. C 2016 Wiley Periodicals, Inc. J. Graph Theory 00: [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] 2016

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“…at least one arc) between them. A k-hypertournament H on n vertices, where 2 ≤ k ≤ n, is a pair H = (V H , A H ), where V H is the vertex set of H and A H is a set of k-tuples of vertices such that, for all subsets S ⊆ V H with |S| = k, A H contains exactly one permutation of S. In [9], Moon proved that every strong tournament is vertex-pancyclic; in [2], Bang-Jensen and Gutin state that this result can be extended for strong semicomplete digraphs; and in [8], Li et al extended Moon's result to k-hypertournaments on n vertices, where 3 ≤ k ≤ n−2.…”

Section: Introductionmentioning

confidence: 99%