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, Dujmović, Morin and Wood. The proof combines (elementary) geometric, combinatorial, algebraic and probabilistic arguments.
Bibliographical notePublisher Copyright:
©2014 Elsevier B.V. All rights reserved.
- Degenerate drawing of a graph
- Distance number of a graph
- Outerplanar graphs