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On the perfect matching graph defined by a set of cycles

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Abstract

The perfect matching graph of a graph G, denoted by M(G), has one vertex for each perfect matching of G and two matchings are adjacent if their symmetric difference is a cycle of G. Let C be a family of cycles of G. The perfect matching graph defined by C is the spanning subgraph M(G, C) of M(G) in which two perfect matchings L and N are adjacent only if \(L \varDelta N\) lies in C. We give a necessary condition and a sufficient condition for M(G, C) to be connected. We also give examples of graphs and of families of cycles for which the sufficient condition is satisfied.

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Authors and Affiliations

  1. Instituto Tecnológico Autónomo de México, Calle Río Hondo 1, Alvaro Obregón, Progreso Tizapán, 01080, Mexico City, D.F., Mexico

    Ana Paulina Figueroa

  2. Universidad Autónoma Metropolitana - Cuajimalpa, Av. Vasco de Quiroga 4871, Cuajimalpa de Morelos, Santa Fe Cuajimalpa, 05348, Mexico City, D.F., Mexico

    Julián Fresán-Figueroa

  3. Universidad Autónoma Metropolitana - Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, Iztapalapa, 09340, Mexico City, D.F., Mexico

    Eduardo Rivera-Campo

Authors
  1. Ana Paulina Figueroa
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  2. Julián Fresán-Figueroa
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  3. Eduardo Rivera-Campo
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Corresponding author

Correspondence to Ana Paulina Figueroa.

Additional information

Partially supported by CONACyT México, Projects 169407, 178910 and 183210.

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Figueroa, A.P., Fresán-Figueroa, J. & Rivera-Campo, E. On the perfect matching graph defined by a set of cycles. Bol. Soc. Mat. Mex. 23, 549–556 (2017). https://doi.org/10.1007/s40590-015-0079-1

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  • DOI: https://doi.org/10.1007/s40590-015-0079-1

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