# Maximum Weight Triangulation and Its Application on Graph Drawing

## Abstract

In this paper, we investigate the maximum weight triangulation of a polygon inscribed in a circle (simply inscribed polygon). A complete characterization of maximum weight triangulation of such polygons has been obtained. As a consequence of this characterization, an *O*(*n* ^{2}) algorithm for finding the maximum weight triangulation of an inscribed *n*-gon is designed. In case of a regular polygon, the complexity of this algorithm can be reduced to *O*(*n*). We also show that a tree admits a maximum weight drawing if its internal node connects at most 2 non-leaf nodes. The drawing can be done in *O*(*n*) time. Furthermore, we prove a property of maximum planar graphs which do not admit a maximum weight drawing on any set of convex points.

## Keywords

Span Tree Maximum Weight Minimum Weight Boundary Edge Regular Polygon## Preview

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