Drawing outerplanar graphs
arXiv:1208.0744 · doi:10.1016/j.comgeo.2014.10.006
Abstract
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.
arXiv comment12 Pages, 5 Figures