# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger 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**: CAB G51

**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.

Upcoming talks | All previous talks | Talks by speaker | Upcoming talks in iCal format (beta version!)

Previous talks by year: 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M | admin login