The crossing number of K11 is 100

Authors:
Shengjun Pan;R. Bruce Richter
Affiliations:
Department of Combinatorics & Optimization, University of Waterloo, Waterloo, Ontario, Canada N 2L 3G1;Department of Combinatorics & Optimization, University of Waterloo, Waterloo, Ontario, Canada N 2L 3G1
Venue:
Journal of Graph Theory
Year:
2007

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Abstract

The crossing number of Kn is known forn ≦10. We develop several simple counting propertiesthat we shall exploit in showing by computer thatcr(K11 = 100, which implies thatcr(K12) = 150. We also determine thenumbers of non-isomorphic optimal drawings of K9and K10. © 2007 Wiley Periodicals, Inc. JGraph Theory 56: 128134, 2007