Skip to main content

Graphs of Non-Crossing Perfect Matchings


 Let P n be a set of n=2m points that are the vertices of a convex polygon, and let ℳ m be the graph having as vertices all the perfect matchings in the point set P n whose edges are straight line segments and do not cross, and edges joining two perfect matchings M 1 and M 2 if M 2=M 1−(a,b)−(c,d)+(a,d)+(b,c) for some points a,b,c,d of P n . We prove the following results about ℳ m : its diameter is m−1; it is bipartite for every m; the connectivity is equal to m−1; it has no Hamilton path for m odd, m>3; and finally it has a Hamilton cycle for every m even, m≥4.

This is a preview of subscription content, access via your institution.

Author information



Additional information

Received: October 10, 2000 Final version received: January 17, 2002


ID="*" Partially supported by Proyecto DGES-MEC-PB98-0933

Acknowledgments. We are grateful to the referees for comments that helped to improve the presentation of the paper.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Hernando, C., Hurtado, F. & Noy, M. Graphs of Non-Crossing Perfect Matchings. Graphs Comb 18, 517–532 (2002).

Download citation

  • Key words. Perfect matching, Non-crossing configuration, Gray code