On Unicyclic Graphs with Uniquely Restricted Maximum Matchings

Vadim E. Levit; Eugen Mandrescu

doi:10.1007/s00373-012-1230-7

On Unicyclic Graphs with Uniquely Restricted Maximum Matchings

Vadim E. Levit
, Eugen Mandrescu

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Pages (from-to)	1867-1879
Number of pages	13
Journal	Graphs and Combinatorics
Volume	29
Issue number	6
DOIs	https://doi.org/10.1007/s00373-012-1230-7
State	Published - Nov 2013
Externally published	Yes

Keywords

Bipartite graph
Greedoid
Local maximum stable set
Unicyclic graph
Uniquely restricted maximum matching

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10.1007/s00373-012-1230-7

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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, μr(G) ≤ μ(G), where μr(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 μr(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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N2 - 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, μr(G) ≤ μ(G), where μr(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 μr(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.

AB - 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, μr(G) ≤ μ(G), where μr(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 μr(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.

KW - Bipartite graph

KW - Greedoid

KW - Local maximum stable set

KW - Unicyclic graph

KW - Uniquely restricted maximum matching

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On Unicyclic Graphs with Uniquely Restricted Maximum Matchings

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Keywords

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