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 Key Takeaways
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Objective & Hypothesis: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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Key Findings & Data: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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Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
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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Cite This Article
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
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