ON THE NUMBER OF GRAPHS WITHOUT LARGE CLIQUES

被引：6

作者：

Mousset, Frank ^{[1
]}

Nenadov, Rajko ^{[1
]}

Steger, Angelika ^{[1
]}

机构：

[1] ETH, Inst Theoret Comp Sci, CH-8092 Zurich, Switzerland

来源：

SIAM JOURNAL ON DISCRETE MATHEMATICS | 2014年 / 28卷 / 04期

关键词：

graph theory; asymptotic counting; clique-free graphs; ASYMPTOTIC STRUCTURE;

D O I：

10.1137/130947878

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In 1976 Erdos, Kleitman, and Rothschild determined asymptotically the logarithm of the number of graphs without a clique of a fixed size l. In this note we extend their result to the case of forbidden cliques of increasing size. More precisely we prove that for l(n) <= (log n)(1/4)/2 there are 2((1-1/(ln - 1))n2/2+o(n2/ln))K(ln)-free graphs of order n. Our proof is based on the recent hypergraph container theorems of Saxton and Thomason and Balogh, Morris, and Samotij, in combination with a theorem of Lovasz and Simonovits.

引用

页码：1980 / 1986

页数：7

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