, Volume 18, Issue 3, pp 517-532

Graphs of Non-Crossing Perfect Matchings

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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.

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.