Using the incompressibility method to obtain local lemma results for Ramsey-type problems

Authors:
Pascal Schweitzer
Affiliations:
Max-Planck-Institut für Informatik, Campus E1 4, 66123 Saarbrücken, Germany
Venue:
Information Processing Letters
Year:
2009

Citing 2
Cited 2

An introduction to Kolmogorov complexity and its applications (2nd ed.)

An introduction to Kolmogorov complexity and its applications (2nd ed.)
An application of Lovász' local lemma‐A new lower bound for the van der Waerden number

Random Structures & Algorithms

A constructive proof of the general lovász local lemma

Journal of the ACM (JACM)
On the paper of Pascal Schweitzer concerning similarities between incompressibility methods and the Lovász Local Lemma

Information Processing Letters

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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.