Abstract
For every fixed integers r, s satisfying 2 ≤ r < s there exists some ε = ε(r, s) > 0 for which we construct explicitly an infinite family of graphs H r,s,n , where H r,s,n has n vertices, contains no clique on s vertices and every subset of at least n 1-ε of its vertices contains a clique of size r. The constructions are based on spectral and geometric techniques, some properties of Finite Geometries and certain isoperimetric inequalities.
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Supported in part by the Fund for Basic Research administered by the Israel Academy of Sciences
Supported in part by a Charles Clore Fellowship
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Alon, N., Krivelevich, M. Constructive Bounds for a Ramsey-Type Problem. Graphs and Combinatorics 13, 217–225 (1997). https://doi.org/10.1007/BF03352998
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DOI: https://doi.org/10.1007/BF03352998