TY - JOUR

T1 - On smoothed analysis in dense graphs and formulas

AU - Krivelevich, Michael

AU - Sudakov, Benny

AU - Tetali, Prasad

PY - 2006/9

Y1 - 2006/9

N2 - We study a model of random graphs, where a random instance is obtained by adding random edges to a large graph of a given density. The research on this model has been started by Bohman and colleagues (Random Struct Algor 22 (2003), 33-42; Random Struct Algor 24 (2004), 105-117). Here we obtain a sharp threshold for the appearance of a fixed subgraph and for certain Ramsey properties. We also consider a related model of random &-SAT formulas, where an instance is obtained by adding random k-clauses to a fixed formula with a given number of clauses, and derive tight bounds for the non-satisfiability of the thus-obtained random formula.

AB - We study a model of random graphs, where a random instance is obtained by adding random edges to a large graph of a given density. The research on this model has been started by Bohman and colleagues (Random Struct Algor 22 (2003), 33-42; Random Struct Algor 24 (2004), 105-117). Here we obtain a sharp threshold for the appearance of a fixed subgraph and for certain Ramsey properties. We also consider a related model of random &-SAT formulas, where an instance is obtained by adding random k-clauses to a fixed formula with a given number of clauses, and derive tight bounds for the non-satisfiability of the thus-obtained random formula.

UR - http://www.scopus.com/inward/record.url?scp=33748437354&partnerID=8YFLogxK

U2 - 10.1002/rsa.20097

DO - 10.1002/rsa.20097

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AN - SCOPUS:33748437354

SN - 1042-9832

VL - 29

SP - 180

EP - 193

JO - Random Structures and Algorithms

JF - Random Structures and Algorithms

IS - 2

ER -