Liu, Yu-RuMurty, M. Ram2023-10-032023-10-032005-07https://doi.org/10.1016/j.jcta.2004.11.004http://hdl.handle.net/10012/19982This article is made available through Elsevier's open archive. This article is available here: https://doi.org/10.1016/j.jcta.2004.11.004 © 2004 Elsevier Inc. All rights reserved.We develop the Turán sieve and a ‘simple sieve’ in the context of bipartite graphs and apply them to various problems in combinatorics. More precisely, we provide applications in the cases of characters of abelian groups, vertex-colourings of graphs, Latin squares, connected graphs, and generators of groups. In addition, we give a spectral interpretation of the Turán sieve.enTuran sievesimple sievecombinatorial sieveArticle