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

We reveal a connection between the incompressibility method and the Lovász 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 . The method is applicable to obtain lower bounds of Ramsey numbers, large transitive subtournaments and other Ramsey phenomena as well.