An Upper Bound for the Transversal Number of Connected k-Uniform Hypergraphs

作     者：Zi-An Chen Bin Chen Zi-An Chen;Bin Chen

作者机构：Center for Discrete MathematicsFuzhou UniversityFuzhou350108FujianChina 

出 版 物：《Journal of the Operations Research Society of China》 (中国运筹学会会刊（英文）)

年 卷 期：2024年第12卷第3期

页      面：829-835页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the National Natural Science Foundation of China(No.12171089) 

主　　题：Transversal number k-uniform hypergraph Perfect matching 

摘      要：Let H be a hypergraph with vertex set V(H)and hyperedge set E(H).We call a vertex set R ■V(H)a transversal if it has a nonempty intersection with every hyperedge of *** transversal number,denoted by τ(H),is the minimum cardinality of *** 2021,Diao verified that the upper bound of transversal number for any connected 3-uniform hypergraph H is at most 2m+1/3,that is,τ(H)≤2m+1/3, where m is the size of ***,they gave the necessary and sufficient conditions to reachthe upper bound,namely τ(H)≤2m+1/3,if and only if H is a hypertreewitha 3 perfect *** this paper,we investigate the transversal number of connected kunifom hypergraphs for k≥*** confrm that τ(H)≤(k-1)m+1/k for any k-unifom hypegraphH with size ***,we show that τ(H)≤(k-1)m+1/k if and only if H is a hypertree with a perfect matching,which generalizes the results of Diao.