# Upper Bound on Dilation of Triangulations of Cyclic Polygons

Conference paper

## Abstract

Given a planar graph G, the dilation between two points of a Euclidean graph is defined as the ratio of the length of the shortest path between the points to the Euclidean distance between the points. The dilation of a graph is defined as the maximum over all vertex pairs (u,v) of the dilation between u and v. In this paper we consider the upper bound on the dilation of triangulation over the set of vertices of a cyclic polygon. We have shown that if the triangulation is a fan (i.e. every edge of the triangulation starts from the same vertex), the dilation will be at most approximately 1.48454. We also show that if the triangulation is a star the dilation will be at most 1.18839.

## Keywords

Short Path Planar Graph Delaunay Triangulation Convex Polygon Arbitrary Vertex
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© Springer-Verlag Berlin Heidelberg 2006