摘要
A hypergraph H is an(n,m)-hypergraph if it contains n vertices and m hyperedges,where n≥1 and m≥0 are two integers.Let k be a positive integer and let L be a set of nonnegative integers.A hyper graph H is k-uniform if all its hyperedges have the same size k,and H is L-intersecting if the number of common vertices of every two hyperedges belongs to L.In this paper,we propose and investigate the problem of estimating the maximum k among all k-uniform L-intersecting(n,m)-hypergraphs for fixed n,m and L.We will provide some tight upper and lower bounds on k in terms of n,m and L.
基金
Supported by National Natural Science Foundation of China(Grant Nos.12242111,12131013,12171393,12071370,71973103,U1803263,11601430)
Natural Science Foundation of Shaanxi Province(Grant Nos.2021JM-040,2020JQ-099)
Shaanxi Fundamental Science Research Project for Mathematics and Physics(Grant No.22JSZ009)
Guangdong Basic and Applied Basic Research Foundation(Grant Nos.2023A1515030208,2022A1515010899)
the Fundamental Research Funds for the Central Universities。
