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On ramsey-tuŕan numbers for 3-graphs

✍ Scribed by A. F. Sidorenko

Publisher
John Wiley and Sons
Year
1992
Tongue
English
Weight
255 KB
Volume
16
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

For every r‐graph G let π(G) be the minimal real number ϵ such that for every ϵ < 0 and n ϵ n~0~(λ, G) every R‐graph H with n vertices and more than (π + ϵ)(nr) edges contains a copy of G. The real number λ(G) is defined in the same way, adding the constraint that all independent sets of vertices in H have size 0(n). Erdös and Sós asked whether there exist r‐graphs G with π(G) < λ(G) < 0. Frankl and Rödl proved that there exist infinitely many such r‐graphs for every r ≦ 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.

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