Abstract.
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.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: October 10, 2000 Final version received: January 17, 2002
RID="*"
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
About this article
Cite this article
Hernando, C., Hurtado, F. & Noy, M. Graphs of Non-Crossing Perfect Matchings. Graphs Comb 18, 517–532 (2002). https://doi.org/10.1007/s003730200038
Issue Date:
DOI: https://doi.org/10.1007/s003730200038