Let 3 ≤ r < s be fixed integers and let G be a graph on n vertices not containing a complete graph on s vertices. The main aim of this paper is to provide a new lower bound on the size of the maximum subset of G without a copy of complete graph Kr. Our results substantially improve previous bounds of Krivelevich and Bollobás and Hind.
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Tel Aviv Univ, Raymond & Beverly Sackler Fac Exact Sci, Dept Math, IL-69978 Tel Aviv, IsraelTel Aviv Univ, Raymond & Beverly Sackler Fac Exact Sci, Dept Math, IL-69978 Tel Aviv, Israel
Alon, N
Pach, J
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机构:Tel Aviv Univ, Raymond & Beverly Sackler Fac Exact Sci, Dept Math, IL-69978 Tel Aviv, Israel
Pach, J
Solymosi, J
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机构:Tel Aviv Univ, Raymond & Beverly Sackler Fac Exact Sci, Dept Math, IL-69978 Tel Aviv, Israel