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Organizers |
Realizations of Configurations
by
Tomaž Pisanski
University of Ljubljana, Slovenija
In his dissertation in 1894 E. Steinitz proved that any connected v3 configuration can be drawn in the Euclidean plane with at most one curved line. Based on a construction by H. L. Dorwart and B. Grünbaum from 1992 we are able to produce a sequence of v3 configurations K(n) with the following property: For any integer m there exists an integer N such that for each n > N one has to remove at least m lines from K(n) in order to obtain an incidence structure that has a realization in the real projective plane (and hence in the Euclidean plane). We show how to reconcile this result with the theorem of Steinitz. However, in passing we produce straight-line drawings of various interesting configurations that were obtained as a joint work with numerous co-authors.
Date received: May 2, 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 # caex-69.