In this paper, we define the score of a vertex in an oriented k-hypergraph and then obtain a necessary and sufficient condition for the sequence of non-negative integers $[s_{1,} s_{2} , ^{...} , s_n ]$ to be a score sequence of some oriented k-hypergraph.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:Given two non-negative integers n and k with $n geq k >$ 1, an oriented k-hypergraph on n vertices is a pair (V,A), where V is a set of vertices with |V| = n and A is a set of k-tuples of vertices, called arcs, such that for any k-subset S of V, A contains at most one of the k! k-tuples whose entries belong to S.
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Temel Bulgular & Veri:Given two non-negative integers n and k with $n geq k >$ 1, an oriented k-hypergraph on n vertices is a pair (V,A), where V is a set of vertices with |V| = n and A is a set of k-tuples of vertices, called arcs, such that for any k-subset S of V, A contains at most one of the k! k-tuples whose entries belong to S.
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Sonuç & Katkı:In this paper, we define the score of a vertex in an oriented k-hypergraph and then obtain a necessary and sufficient condition for the sequence of non-negative integers $[s_{1,} s_{2} , ^{...} , s_n ]$ to be a score sequence of some oriented k-hypergraph.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri
Abstract
Given two non-negative integers n and k with $n geq k >$ 1, an oriented k-hypergraph on n vertices is a pair (V,A), where V is a set of vertices with |V| = n and A is a set of k-tuples of vertices, called arcs, such that for any k-subset S of V, A contains at most one of the k! k-tuples whose entries belong to S. In this paper, we define the score of a vertex in an oriented k-hypergraph and then obtain a necessary and sufficient condition for the sequence of non-negative integers $[s_{1,} s_{2} , ^{...} , s_n ]$ to be a score sequence of some oriented k-hypergraph.
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Bu Makaleye Atıf Yap
PİRZADA, S., GUOFEİ, Z. (2022). Score sequences in oriented k-hypergraphs. European Journal of Pure and Applied Mathematics (elektronik), Cilt: 1 - Sayı: 3, 10–20. https://ajindex.com/articles/511440
P. Avery, Score sequences of oriented graphs, J. Graph Theory, Vol. 15, No. 3(1991) 251-257
C. M. Bang and H. Sharp Jr., Score vectors of tournaments, J. Combin.Theory Ser. B 26 (1) (1979) 81-84
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H. G. Landau, On dominance relations and the structure of animal societies. III. The condition for a score structure, Bull. Math. Biophys. 15 ( 1953 ) 143-148
S. Pirzada, T. A. Naikoo and N. A. Shah, Score sequences in oriented graphs, J. Applied Mathematics and Computing (2006), 22(1-2) (2007) 257-268
C. Wang and G. Zhou, Note on the degree sequences of k-hypertournaments, Discrete Mathematics, To appear
G. Zhou, T. Yao and K. Zhang, On score sequences of k-hypertournaments, European J. Combin. 21 (8) (2000) 993-1000.