TY - JOUR
T1 - On Unicyclic Graphs with Uniquely Restricted Maximum Matchings
AU - Levit, Vadim E.
AU - Mandrescu, Eugen
PY - 2013/11
Y1 - 2013/11
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
UR - http://www.scopus.com/inward/record.url?scp=84886512699&partnerID=8YFLogxK
U2 - 10.1007/s00373-012-1230-7
DO - 10.1007/s00373-012-1230-7
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AN - SCOPUS:84886512699
SN - 0911-0119
VL - 29
SP - 1867
EP - 1879
JO - Graphs and Combinatorics
JF - Graphs and Combinatorics
IS - 6
ER -