Graphs and Combinatorics

, Volume 18, Issue 3, pp 517–532

Graphs of Non-Crossing Perfect Matchings

  • C. Hernando
  • F. Hurtado
  • Marc Noy

DOI: 10.1007/s003730200038

Cite this article as:
Hernando, C., Hurtado, F. & Noy, M. Graphs Comb (2002) 18: 517. doi:10.1007/s003730200038

Abstract.

 Let Pn be a set of n=2m points that are the vertices of a convex polygon, and let ℳm be the graph having as vertices all the perfect matchings in the point set Pn whose edges are straight line segments and do not cross, and edges joining two perfect matchings M1 and M2 if M2=M1−(a,b)−(c,d)+(a,d)+(b,c) for some points a,b,c,d of Pn. We prove the following results about ℳm: 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.

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

Copyright information

© Springer-Verlag Tokyo 2002

Authors and Affiliations

  • C. Hernando
    • 1
  • F. Hurtado
    • 2
  • Marc Noy
    • 3
  1. 1.Department de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain. e-mail: hernando@ma1.upc.esES
  2. 2.Department de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Pau Gargallo 5, 08028 Barcelona, Spain. e-mail: hurtadoES
  3. 3.Department de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Pau Gargallo 5, 08028 Barcelona, Spain. e-mail: noy@ma2.upc.esES