TY - JOUR
T1 - Unicycle graphs and uniquely restricted maximum matchings
AU - Levit, Vadim E.
AU - Mandrescu, Eugen
PY - 2005/10/15
Y1 - 2005/10/15
N2 - 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. G is a unicycle graph if it owns only one cycle. Golumbic, Hirst and Lewenstein observed that for a tree or a graph with only odd cycles the size of a maximum uniquely restricted matching is equal to the matching number of the graph. In this paper we characterize unicycle graphs enjoying this equality. Moreover, we describe unicycle graphs with only uniquely restricted maximum matchings. Using these findings, we show that unicycle graphs having only uniquely restricted maximum matchings can be recognized in polynomial time.
AB - 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. G is a unicycle graph if it owns only one cycle. Golumbic, Hirst and Lewenstein observed that for a tree or a graph with only odd cycles the size of a maximum uniquely restricted matching is equal to the matching number of the graph. In this paper we characterize unicycle graphs enjoying this equality. Moreover, we describe unicycle graphs with only uniquely restricted maximum matchings. Using these findings, we show that unicycle graphs having only uniquely restricted maximum matchings can be recognized in polynomial time.
KW - greedoid
KW - local maximum stable set
KW - uniquely restricted matching
UR - http://www.scopus.com/inward/record.url?scp=34247145962&partnerID=8YFLogxK
U2 - 10.1016/j.endm.2005.06.055
DO - 10.1016/j.endm.2005.06.055
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AN - SCOPUS:34247145962
SN - 1571-0653
VL - 22
SP - 261
EP - 265
JO - Electronic Notes in Discrete Mathematics
JF - Electronic Notes in Discrete Mathematics
ER -