Improved bounds for the Erdős-Rogers function
نویسندگان
چکیده
منابع مشابه
Improved bounds for Erdős' Matching Conjecture
Article history: Received 7 June 2012 Available online 24 February 2013
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Extending the concept of Ramsey numbers, Erdős and Rogers introduced the following function. For given integers 2 ≤ s < t let fs,t(n) = min{max{|W | : W ⊆ V (G) and G[W ] contains no Ks}}, where the minimum is taken over all Kt-free graphs G of order n. In this paper, we show that for every s ≥ 3 there exist constants c1 = c1(s) and c2 = c2(s) such that fs,s+1(n) ≤ c1(log n)2 √ n. This result i...
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Let ES(n) denote the least integer such that among any ES(n) points in general position in the plane there are always n in convex position. In 1935, P. Erdős and G. Szekeres showed that ES(n) exists and ES(n) ≤ ` 2n−4 n−2 ́ + 1. Six decades later, the upper bound was slightly improved by Chung and Graham, a few months later it was further improved by Kleitman and Pachter, and another few months ...
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The well-known Ramsey number R(t, u) is the smallest integer n such that every Kt-free graph of order n contains a subset of u vertices with no K2. Erdős and Rogers considered a more general problem replacing K2 by Ks for 2 ≤ s < t. Extending the problem of determining Ramsey numbers they defined the following function fs,t(n) = min { max{|S| : S ⊆ V (H) and H[S] contains no Ks} } , where the m...
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ژورنال
عنوان ژورنال: Advances in Combinatorics
سال: 2020
ISSN: 2517-5599
DOI: 10.19086/aic.12048