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KNOTS in WASHINGTON XV (2nd Japan-USA Workshop in Knot Theory)
January 10-15, 2003
George Washington University and Johns Hopkins University
Washington, DC and Baltimore, MD, USA

Organizers
Kazuaki Kobayashi, Jozef H. Przytycki, Yongwu Rong, Shin-ichi Suzuki, Kouki Taniyama, Tatsuya Tsukamoto, Akira Yasuhara

Conference Homepage


On Zarankiewicz's conjecture regarding the crossing number of K_p, q
by
Paul C. Kainen
Department of Mathematics, Georgetown University

The crossing number of a graph is the least number of edge-intersections with which the graph can be drawn in the plane (subject to a few mild conditions). For the complete bipartite graph, the problem has an interesting history which will be briefly sketched, including a false proof in Zarankiewicz's original paper of a particular value for this crossing number. A new drawing scheme will be described which may show that the conjectured value is too large.

Date received: January 10, 2003

Copyright © 2003 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cajr-37.