Drawing outerplanar graphs using thirteen edge lengths

Abstract

We show that every outerplanar graph $G$ can be linearly embedded in the plane such that the number of distinct distances between pairs of adjacent vertices is at most thirteen and there is no intersection between the image of a vertex and that of an edge not containing it. This extends the work of Alon and the second author, where only overlap between vertices was disallowed, thus settling a problem posed by Carmi, Dujmović, Morin and Wood.

22 pages, 5 figures. Title changed from "Drawing outerplanar graphs using finitely many edge lengths"