Noga Alon, Ohad Noy Feldheim
Published 2012-08-03Version 1
It is shown that for any outerplanar graph G there is a one to one mapping of the vertices of G to the plane, so that the number of distinct distances between pairs of connected vertices is at most three. This settles a problem of Carmi, Dujmovic, Morin and Wood. The proof combines (elementary) geometric, combinatorial, algebraic and probabilistic arguments.
Comments: 12 Pages, 5 Figures
Drawing outerplanar graphs using finitely many edge lengths
On Distinct Distances Between a Variety and a Point Set
On lattices, distinct distances, and the Elekes-Sharir framework
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