TY - GEN

T1 - Quasi-randomness is determined by the distribution of copies of a fixed graph in equicardinal large sets

AU - Yuster, Raphael

PY - 2008

Y1 - 2008

N2 - For every fixed graph H and every fixed 0 < α < 1, we show that if a graph G has the property that all subsets of size αn contain the "correct" number of copies of H one would expect to find in the random graph G(n,p) then G behaves like the random graph G(n,p); that is, it is p-quasi-random in the sense of Chung, Graham, and Wilson [4].This solves a conjecture raised by Shapira [8] and solves in a strong sense an open problem of Simonovits and Sós [9].

AB - For every fixed graph H and every fixed 0 < α < 1, we show that if a graph G has the property that all subsets of size αn contain the "correct" number of copies of H one would expect to find in the random graph G(n,p) then G behaves like the random graph G(n,p); that is, it is p-quasi-random in the sense of Chung, Graham, and Wilson [4].This solves a conjecture raised by Shapira [8] and solves in a strong sense an open problem of Simonovits and Sós [9].

UR - http://www.scopus.com/inward/record.url?scp=51849126511&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-85363-3_47

DO - 10.1007/978-3-540-85363-3_47

M3 - Conference contribution

AN - SCOPUS:51849126511

SN - 3540853626

SN - 9783540853626

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 596

EP - 601

BT - Approximation, Randomization and Combinatorial Optimization

T2 - 11th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2008 and 12th International Workshop on Randomization and Computation, RANDOM 2008

Y2 - 25 August 2008 through 27 August 2008

ER -