Math 233 : Non - constructive methods in combinatorics

Abstract

Given underlying independent random variables X1, ..., Xm with product measure μ. The “bad events” E1, ..., En are each determined by a certain subset of the random variables, which we denote var(Ei) ⊂ [n]. The dependency graph G has vertices [n] and edges (i, j) ∈ E(G) whenever var(Ei) ∩ var(Ej) 6= ∅. Note that this is a valid choice of a dependency graph, since each event Ei is independent of any conditioning on the variables outside of var(Ei). Given that the conditions of the Lovász Local Lemma (or Shearer’s Lemma) hold, we want to find a realization of the random variables X1, ..., Xm such that no events Ei happen.

Cite this paper

@inproceedings{Vondrak2016Math2, title={Math 233 : Non - constructive methods in combinatorics}, author={Jan Vondrak and Huy Pham}, year={2016} }