Difference sequences for crossings
by
Michael Prestidge
University of Auckland

The ``crossing number'' of a graph G on a surface S is the smallest number of edge-crossings in any drawing of G on S. This talk investigates how adding handles to S can affect this crossing number. Specifically, possible ``difference sequences'' d₁, d₂, d₃, ... will be examined where d_i denotes the difference between the crossing number of G on a surface of genus i and on a surface of genus i-1. Of particular interest will be increasing difference sequences. The talk will extend known boundaries for such sequences and display new possibilities. In addition, several issues for further research will be announced and techniques for addressing them introduced.

Date received: November 22, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafp-31.