One Turán Type Problem on Uniform Hypergraphs

Autor: Linlin Wang, Sujuan Liu
Jazyk: angličtina
Rok vydání: 2024
Předmět:
Zdroj: Axioms, Vol 13, Iss 8, p 544 (2024)
Druh dokumentu: article
ISSN: 2075-1680
DOI: 10.3390/axioms13080544
Popis: 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 er(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 er(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 er(n,m;p) by applying the lower bound of the independent set of a hypergraph.
Databáze: Directory of Open Access Journals
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