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On Unicyclic Graphs with Uniquely Restricted Maximum Matchings

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Abstract

A graph is called unicyclic if it owns only one cycle. A matching M is called uniquely restricted in a graph G if it is the unique perfect matching of the subgraph induced by the vertices that M saturates. Clearly, μ r (G) ≤ μ(G), where μ r (G) denotes the size of a maximum uniquely restricted matching, while μ(G) equals the matching number of G. In this paper we study unicyclic bipartite graphs enjoying μ r (G) = μ(G). In particular, we characterize unicyclic bipartite graphs having only uniquely restricted maximum matchings. Finally, we present some polynomial time algorithms recognizing unicyclic bipartite graphs with (only) uniquely restricted maximum matchings.

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Authors and Affiliations

  1. Department of Computer Science and Mathematics, Ariel University Center of Samaria, Ariel, Israel

    Vadim E. Levit

  2. Department of Computer Science, Holon Institute of Technology, Holon, Israel

    Eugen Mandrescu

Authors
  1. Vadim E. Levit
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  2. Eugen Mandrescu
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Corresponding author

Correspondence to Vadim E. Levit.

Additional information

A preliminary version of this paper was presented at 7th International Colloquium on Graph Theory, ICGT ’05, Hyères, France; an extended abstract has been published in [11].

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Levit, V.E., Mandrescu, E. On Unicyclic Graphs with Uniquely Restricted Maximum Matchings. Graphs and Combinatorics 29, 1867–1879 (2013). https://doi.org/10.1007/s00373-012-1230-7

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  • DOI: https://doi.org/10.1007/s00373-012-1230-7

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