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