A New Proof of the Nešetřil-Rödl Theorem

Abstract

In this paper we give a new proof of the Nešetřil-Rödl Theorem, a deep result of discrete mathematics which is one of the cornerstones of the structural Ramsey theory. In contrast to the well-known proofs which employ intricate combinatorial strategies, this proof is spelled out in the language of category theory and the main result follows by applying several simple categorical constructions. The gain from the approach we present here is that, instead of giving the proof in the form of a large combinatorial construction, we can start from a few building blocks and then combine them into the final proof using general principles.