Zarankiewicz's Conjecture is finite for each fixed m

  • Authors:

  • Robin Christian;R. Bruce Richter;Gelasio Salazar

  • Affiliations:

  • University of Waterloo, Waterloo, ON, N2L 3G1, Canada;University of Waterloo, Waterloo, ON, N2L 3G1, Canada;Universidad Autonoma de San Luis Potosi, San Luis Potosi, SLP 78000, Mexico

  • Venue:
  • Journal of Combinatorial Theory Series B
  • Year:
  • 2013

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Abstract

Zarankiewicz@?s Crossing Number Conjecture states that the crossing number cr(K"m","n) of the complete bipartite graph K"m","n equals Z(m,n):=@?m/2@?@?(m-1)/2@?@?n/2@?@?(n-1)/2@?, for all positive integers m, n. This conjecture has only been verified for min{m,n}=