On the stability of the Erdos-Ko-Rado theorem

被引：35

作者：

Bollobas, Bela ^{[1
,2
,3
]}

Narayanan, Bhargav P. ^{[1
]}

Raigorodskii, Andrei M. ^{[4
,5
]}

机构：

[1] Univ Cambridge, Dept Pure Math & Math Stat, Cambridge CB3 OWB, England

[2] Univ Memphis, Dept Math Sci, Memphis, TN 38152 USA

[3] London Inst Math Sci, London W1K 2XF, England

[4] Moscow MV Lomonosov State Univ, Mech & Math Fac, Dept Math Stat & Random Proc, Moscow 119991, Russia

[5] Moscow Inst Phys & Technol, Fac Innovat & High Technol, Dolgoprudnyi 141700, Moscow Region, Russia

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES A | 2016年 / 137卷

基金：

美国国家科学基金会; 俄罗斯基础研究基金会;

关键词：

Intersecting families; Stability; Transference; Random graphs; RAMSEY PROPERTIES; ARITHMETIC PROGRESSIONS; INTERSECTION-THEOREMS; EXTREMAL SUBGRAPHS; RANDOM HYPERGRAPHS; RANDOM GRAPHS; FINITE SETS; SYSTEMS; FAMILIES; SUBSETS;

D O I：

10.1016/j.jcta.2015.08.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Delete the edges of a Kneser graph independently of each other with some probability: for what probabilities is the independence number of this random graph equal to the independence number of the Kneser graph itself? We prove a sharp threshold result for this question in certain regimes. Since an independent set in the Kneser graph is the same as an intersecting (uniform) family, this gives us a random analogue of the Erdos-Ko-Rado theorem. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：64 / 78

页数：15

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