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Graphs of Triangulations and Perfect Matchings

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Abstract

Given a set P of points in general position in the plane, the graph of triangulations 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 of , 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 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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Authors and Affiliations

  1. National Institute of Informatics, Tokyo, Japan

    M.E. Houle

  2. Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, España

    F. Hurtado & M. Noy

  3. Departamento de Matemáticas, Universidad Autónoma Metropolitana-Iztapalapa, México

    E. Rivera-Campo

Authors
  1. M.E. Houle
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  2. F. Hurtado
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  3. M. Noy
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  4. E. Rivera-Campo
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Corresponding author

Correspondence to M.E. Houle.

Additional information

Dedicated to Professor Víctor Neumann-Lara on the occasion of his 70th birthday

Partially supported by Projects DGES-SEUID PB98-0933, MCYT-BFM2001-2340, MCYT-FEDER-BFM2002-0557 and Gen. Cat 2001SGR00224

Part of the research was done while this author was on sabbatical leave visiting the Universitat Politècnica de Catalunya with grants by MECD-España and CONACYT-México

Received: April, 2004

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Houle, M., Hurtado, F., Noy, M. et al. Graphs of Triangulations and Perfect Matchings. Graphs and Combinatorics 21, 325–331 (2005). https://doi.org/10.1007/s00373-005-0615-2

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  • DOI: https://doi.org/10.1007/s00373-005-0615-2

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