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Foundations of Computational Mathematics
A remarkable lemma of Szemerédi asserts that, very roughly speaking, any dense graph can be decomposed into a bounded number of pseudorandom bipartite graphs. This far-reaching result has proved to play a central rôle in many areas of combinatorics, both 'pure' and 'algorithmic.' The quest for an equally powerful variant of this lemma for sparse graphs has not yet been successful, but some progress has been achieved recently. The aim of this note is to report on the successes so far. Partiallydoi:10.1007/978-3-642-60539-0_16 fatcat:4kqy2jga5baylj6qhxsw53nxr4