Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Thursday, April 21, 2011, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Emo Welzl

Kasteleyn and the Number of Crossing-Free Matchings and Cycles on a Planar Point Set

In 1967 Piet Kastelyn showed how to count the number of perfect matchings in a planar graph, simply by looking at the determinant of an appropriate skew symmetric variant of the adjacency matrix. Raimund Seidel observed an extremal combinatorics implication, namely that a planar graph on n vertices has at most sqrt[4]{6}^n perfect matchings (via the Hadamard bound). We show how, for a planar set P of n points, that can be used to relate the number, sc(P), of crossing-free straight-line spanning cycles (simple polygonizations) of P to the number of triangulations, tr(P), of P: sc(P) < sqrt[4]{12}^n tr(P) We conjecture, though, that this can be significantly improved, actually to sc(P)= O(c^n)tr(P) for some constant c < 1.

Joint work with Micha Sharir and Adam Sheffer.

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