Using the Incompressibility Method to obtain Local Lemma results for Ramsey-type Problems

Details Using the Incompressibility Method to obtain Local Lemma results for Ramsey-type Problems Using the Incompressibility Method to obtain Local Lemma results for Ramsey-type Problems

2008-04-04

arxiv.org/abs/0804.0724v1

Mathematics

Combinatorics

8 pages, 1 figure

Scientific paper

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. It applies to lower bounds of Ramsey numbers, large transitive subtournaments and other Ramsey phenomena as well.

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