Graphs of Triangulations and Perfect Matchings
نویسندگان
چکیده
Given a set P of points in the plane, the graph of triangulations T (P ) of P has a vertex for every triangulation of P , and two of them are adjacent if they differ by a single edge exchange. We prove that the subgraph TM(P ) of T (P ), consisting of all triangulations of P that admit a perfect matching, is connected. A main tool in our proof is a result of independent interest, namely that the graph M(P ) that has as vertices the non-crossing perfect matchings of P and two of them are adjacent if their symmetric difference is a single non-crossing cycle, is also connected.
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عنوان ژورنال:
- Graphs and Combinatorics
دوره 21 شماره
صفحات -
تاریخ انتشار 2005