Improved bounds for the crossing numbers of Km,n and Kn

• Main Authors: Klerk, Etienne de., Pasechnik, Dmitrii V., Maharry, J., Richter, R. B., Salazar, G.
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2011
• Subjects: DRNTU::Science::Mathematics::Applied mathematics
• Online Access: https://hdl.handle.net/10356/100823; http://hdl.handle.net/10220/6787
• Institution: Nanyang Technological University

It has been long conjectured that the crossing number cr(Km,n) of the complete bipartite graph Km,n equals the Zarankiewicz number Z(m, n) :=[(m-1)/2][m/2][(n-1)/2][n/2]. Another longstanding conjecture states that the crossing number cr(Kn) of the complete graph Kn equals Z(n):=(1/4)[n/2][(n-1)/2][...