典型文献
On the Sizes of k-edge-maximal r-uniform Hypergraphs
文献摘要：
Let H=(V,E)be a hypergraph,where V is a set of vertices and E is a set of non-empty subsets of V called edges.If all edges of H have the same cardinality r,then H is an r-uniform hypergraph;if E consists of all r-subsets of V,then H is a complete r-uniform hypergraph,denoted by Krn,where n=|V|.A hypergraph H'=(V',E')is called a subhypergraph of H=(V,E)if V'C V and E'? E.The edge-connectivity of a hypergraph H is the cardinality of a minimum edge set F ? E such that H-F is not connected,where H-F=(V,E \ F).An r-uniform hypergraph H=(V,E)is k-edge-maximal if every subhypergraph of H has edge-connectivity at most k,but for any edge e ∈ E(Krn)\ E(H),H+e contains at least one subhypergraph with edge-connectivity at least k+1.Let k and r be integers with k≥2 and r≥2,and let t=t(k,r)be the largest integer such that(t-1r-1)≤k.That is,t is the integer satisfying(t-1r-1)≤k＜(t/r-1).We prove that if H is an r-uniform k-edge-maximal hypergraph such that n=|V(H)|≥t,then(i)|E(H)|≤(tr)+(n-t)k,and this bound is best possible;(ⅱ)|E(H)|≥(n-1)k-((t-1)k-(tr))([)n/t」,and this bound is best possible.
文献关键词：
中图分类号：
作者姓名：
Ying-zhi TIAN;Hong-Jian LAI;Ji-xiang MENG;Li-qiong XU
作者机构：
College of Mathematics and System Sciences,Xinjiang University,Urumqi 830046,China;Department of Mathematics,West Virginia University,Morgantown,WV 26506,USA;School of Science,Jimei University,Xiamen 361021,China
文献出处：
引用格式：
[1]Ying-zhi TIAN;Hong-Jian LAI;Ji-xiang MENG;Li-qiong XU-.On the Sizes of k-edge-maximal r-uniform Hypergraphs)[J].应用数学学报（英文版）,2022(03):532-539
A类：
Hypergraphs,Krn,subhypergraph,H+e
B类：
On,Sizes,maximal,uniform,Let,where,vertices,empty,subsets,called,edges,If,have,same,cardinality,then,consists,complete,denoted,by,connectivity,minimum,such,that,connected,An,every,has,most,but,any,contains,least,one,k+1,integers,largest,1r,That,satisfying,We,prove,tr,this,bound,best,possible
AB值：
0.329578
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