The size of the giant high-order component in random hypergraphs

被引：12

作者：

Cooley, Oliver ^{[1
]}

Kang, Mihyun ^{[1
]}

Koch, Christoph ^{[1
]}

机构：

[1] Graz Univ Technol, Inst Discrete Math, Steyrergasse 30, A-8010 Graz, Austria

来源：

RANDOM STRUCTURES & ALGORITHMS | 2018年 / 53卷 / 02期

基金：

奥地利科学基金会;

关键词：

branching process; degree; giant component; high-order connectedness; phase transition; random hypergraphs; PHASE-TRANSITION; EVOLUTION;

D O I：

10.1002/rsa.20761

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

The phase transition in the size of the giant component in random graphs is one of the most well-studied phenomena in random graph theory. For hypergraphs, there are many possible generalizations of the notion of a connected component. We consider the following: two j-sets (sets of j vertices) are j-connected if there is a walk of edges between them such that two consecutive edges intersect in at least j vertices. A hypergraph is j-connected if all j-sets are pairwise j-connected. In this paper, we determine the asymptotic size of the unique giant j-connected component in random k-uniform hypergraphs for any k3 and 1j <= k-1.

引用

页码：238 / 288

页数：51

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