Paper Info
Title
Using the incompressibility method to obtain local lemma results for Ramsey-type problems
Abstract
We reveal a connection between the incompressibility method and the Lovasz local lemma in the context of Ramsey theory. We obtain bounds by repeatedly encoding objects of interest and thereby compressing strings. The method is demonstrated on the example of van der Waerden numbers. In particular we reprove that w(k;c)=c^k^-^3k@?k-1k. The method is applicable to obtain lower bounds of Ramsey numbers, large transitive subtournaments and other Ramsey phenomena as well.
Year
DOI
Venue
2009
10.1016/j.ipl.2008.09.030
Inf. Process. Lett.
Keywords
Field
DocType
ramsey theory,encoding object,ramsey phenomenon,ramsey number,lower bound,local lemma result,lovasz local lemma,ramsey-type problem,incompressibility,incompressibility method,data compression,compressing string,van der waerden number,large transitive subtournaments,algorithms
Ramsey theory,Discrete mathematics,Combinatorics,Upper and lower bounds,Ramsey's theorem,Van der Waerden's theorem,Lovász local lemma,Mathematics,Lemma (mathematics),Transitive relation
Journal
Volume
Issue
ISSN
109
4
0020-0190
Citations 
PageRank 
References 
3
0.84
2
Authors
1
Name
Order
Citations
PageRank
Pascal Schweitzer121416.94