TY - JOUR

T1 - On the Probability of Independent Sets in Random Graphs

AU - Krivelevich, Michael

AU - Sudakov, Benny

AU - Vu, Van H.

AU - Wormald, Nicholas C.

PY - 2003/1

Y1 - 2003/1

N2 - Let k be the asymptotic value of the independence number of the random graph G(n, p). We prove that if the edge probability p(n) satisfies p(n) ≫ n-2/5ln6/5n then the probability that G(n, p) does not contain an independent set of size k - c, for some absolute constant c > 0, is at most exp{ -cn2/(k4p)}. We also show that the obtained exponent is tight up to logarithmic factors, and apply our result to obtain new bounds on the choice number of random graphs. We also discuss a general setting where our approach can be applied to provide an exponential bound on the probability of certain events in product probability spaces.

AB - Let k be the asymptotic value of the independence number of the random graph G(n, p). We prove that if the edge probability p(n) satisfies p(n) ≫ n-2/5ln6/5n then the probability that G(n, p) does not contain an independent set of size k - c, for some absolute constant c > 0, is at most exp{ -cn2/(k4p)}. We also show that the obtained exponent is tight up to logarithmic factors, and apply our result to obtain new bounds on the choice number of random graphs. We also discuss a general setting where our approach can be applied to provide an exponential bound on the probability of certain events in product probability spaces.

UR - http://www.scopus.com/inward/record.url?scp=0037234549&partnerID=8YFLogxK

U2 - 10.1002/rsa.10063

DO - 10.1002/rsa.10063

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0037234549

SN - 1042-9832

VL - 22

SP - 1

EP - 14

JO - Random Structures and Algorithms

JF - Random Structures and Algorithms

IS - 1

ER -