Ear Decomposition of Factor-critical Graphs and Number of Maximum Matchings
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چکیده
A connected graph G is said to be factor-critical if G − v has a perfect matching for every vertex v of G. Lovász proved that every factor-critical graph has an ear decomposition. In this paper, the ear decomposition of the factor-critical graphs G satisfying that G− v has a unique perfect matching for any vertex v of G with degree at least 3 is characterized. From this, the number of maximum matchings of factor-critical graphs with the special ear decomposition is obtained.
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تاریخ انتشار 2013