Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, November 24, 2005, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Emo Welzl

Random Triangulations of Point Sets

Given a set of n points in the plane, we consider triangulations drawn uniformly at random from all triangulations of the point set, and we derive bounds (in terms of n) on the expected number of vertices of given degree k, for k=3,4,.... For degree 3 vertices, lower and upper bounds are n/43 and 2n/5, respectively (note that the number of degree 3 vertices in a triangulation may vary between 0 and 2n/3). We also show how these bounds can be employed to infer an upper bound on the number of triangulations n points can have, improving on previous work by Santos and Seidel.

(Joint work with Micha Sharir.)

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