Constructive Bounds for a Ramsey-Type Problem | Zendy

Noga Alon | Zendy; Michael Krivelevich | Zendy

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Constructive Bounds for a Ramsey-Type Problem

Author(s) -

Noga Alon,

Michael Krivelevich

Publication year - 1997

Publication title -

graphs and combinatorics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.59

H-Index - 40

eISSN - 1435-5914

pISSN - 0911-0119

DOI - 10.1007/bf03352998

Subject(s) - mathematics , combinatorics , isoperimetric inequality , constructive , clique number , type (biology) , discrete mathematics , graph , ecology , process (computing) , computer science , biology , operating system

For every fixed integers r, s satisfying 2 ≤ r < s there exists some ¿ = ¿(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-¿ 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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