Drawing outerplanar graphs using thirteen edge lengths

Drawing outerplanar graphs using three edge lengths

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.

Drawing outerplanar graphs

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.

Drawing some 4-regular planar graphs with integer edge lengths

A classic result of Fáry states that every planar graph can be drawn in the plane without crossings using only straight line segments. Harborth et al. conjecture that every planar graph has such a drawing where every edge length is integral. Biedl proves that every planar graph of maximum degree 4 that is not 4-regular has such a straight-line embedding, but the techniques are insufficient for ...

Drawing some planar graphs with integer edge-lengths

In this paper, we study drawings of planar graphs such that all edge lengths are integers. It was known that such drawings exist for all planar graphs with maximum degree 3. We give a different proof of this result, which is based on a simple transformation of hexagonal drawings as created by Kant. Moreover, if the graph is 3-connected then the vertices have integer coordinates that are in O(n)...

List Edge Colorings of Outerplanar Graphs