Mathematics Research Projects

Project 10: Triangulation of Plane Polygons


a. Can every plane (non-self-intersecting) polygon be triangulated to form a graph where every vertex has valence at most s? (Or, can you find a family of polygons Pt such that for every triangulation of Pt there is a vertex of valence at least t?)

b. Can you find a family of plane (non-self-intersecting) polygons Pt which have exactly t ways to triangulate the polygon?

c. Explore the possibility of some connection between the number of guards of a polygon and number of different ways to triangulate the polygon. (The number of guards for a polygon is the minimum number of points in the polygon from which all of the polygon is collectively visible from one or more of the points.)

(See Project 1.)


1. O'Rourke, J., Art Gallery Theorems and Algorithms, Oxford University Press, New York, 1987.

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Joseph Malkevitch
Department of Mathematics and Computing
York College (CUNY)
Jamaica, New York 11451-0001
(Comments and results related to the project above are welcome.)

Some of this work was prepared with partial support from the National Science Foundation (Grant Number: DUE 9555401) to the Long Island Consortium for Interconnected Learning (administered by SUNY at Stony Brook, Alan Tucker, Project Director).