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- Title
One Turán Type Problem on Uniform Hypergraphs.
- Authors
Wang, Linlin; Liu, Sujuan
- Abstract
Let n , m , p , r ∈ N with p ≥ n ≥ r . For a hypergraph, if each edge has r vertices, then the hypergraph is called an r-graph. Define e r (n , m ; p) to be the maximum number of edges of an r-graph with p vertices in which every subgraph of n vertices has at most m edges. Researching this function constitutes a Turán type problem. In this paper, on the one hand, for fixed p, we present some results about the exact values of e r (n , m ; p) for small m compared to n; on the other hand, for sufficient large p, we use the combinatorial technique of double counting to give an upper bound of e (n , m ; p) and obtain a lower bound of e r (n , m ; p) by applying the lower bound of the independent set of a hypergraph.
- Subjects
INDEPENDENT sets; HYPERGRAPHS; COUNTING
- Publication
Axioms (2075-1680), 2024, Vol 13, Issue 8, p544
- ISSN
2075-1680
- Publication type
Article
- DOI
10.3390/axioms13080544