Sieve methods in combinatorics

  • Authors:

  • Yu-Ru Liu;M. Ram Murty

  • Affiliations:

  • Department of Pure Mathematics, University of Waterloo, Waterloo, Ont., Canada, N2L 3G1;Department of Mathematics and Statistics, Queen's University, Kingston, Ont., Canada, K7L 3N6

  • Venue:
  • Journal of Combinatorial Theory Series A
  • Year:
  • 2005

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Abstract

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.