ON RAMSEY-TURAN NUMBERS FOR 3-GRAPHS

被引:4
|
作者
SIDORENKO, AF
机构
[1] Moscow, 117333, Leninskiy prospect 52
关键词
D O I
10.1002/jgt.3190160108
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
For every r-graph G let pi(G) be the minimal real number-pi such that for every epsilon > 0 and n > n0(epsilon, G) every r-graph H with n vertices and more than (pi + epsilon)(r(n)) edges contains a copy of G. The real number lambda(G) is defined in the same way, adding the constraint that all independent sets of vertices in H have size o(n). Erdos and Sos asked whether there exist r-graphs G with pi(G) > lambda(G) > 0. Frankl and Rodl proved that there exist infinitely many such r-graphs for every r greater-than-or-equal-to 3. However, no example of an r-graph with above property was known. We construct an example of such a 3-graph with 7 vertices and 9 edges.
引用
收藏
页码:73 / 78
页数:6
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