一致超图的边连通性和最大边连通性  

Edge-connectivity and Maximal Edge-connectivity of Uniform Hypergraphs

作　　者：张磊 牛倩楠 任海珍 ZHANG Lei;NIU Qiannan;REN Haizhen(School of Mathematics and Statistics,Qinghai Normal University,Xi'ning 810008,China)

机构地区：[1]青海师范大学数学与统计学院,青海西宁810008

出　　处：《山西大学学报（自然科学版）》2021年第6期1079-1085,共7页Journal of Shanxi University(Natural Science Edition)

基　　金：青海师范大学自然科学中青年科研基金(2020-QZR-003)。

摘　　要：超图的边连通性与超网络的容错性密切相关,是一个判断超网络可靠性的经典指标。一个连通超图H的边连通度λ(H)是超图H的所有边割中最小边割的大小。用δ(H)表示超图H的最小度,称满足条件λ(H)=δ(H)的超图为最大边连通的。文章用最大度和直径给出了r-一致超图的边连通度的一个下界。进一步获得了r-一致超图是最大边连通的一个充分条件。The edge-connectivity of hypergraphs is related to the fault-tolerance of supernetworks, and is a classical measure of the reliability of the supernetworks. The edge-connectivity λ(H) of a connected hypergraph H is the minimum cardinality among all the edge-cuts of H. Let δ(H) denote the minimum degree of H. Hypergraphs for which λ(H)= δ(H) are called maximally edgeconnected. We give a lower bound of the edge-connectivity of r-uniform hypergraph in terms of the maximum degree and diameter.Furthermore, we obtain a sufficient condition such that an r-uniform hypergraph to be maximal.

关 键 词：超图 边割 边连通性 最大边连通性 

分 类 号：O436[机械工程—光学工程]