Abstract

For every xed integers r; s satisfying 2 r < s there exists some = (r; s) > 0 for which we construct explicitly an innite 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 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. 1

Citations