On the (co)girth of connected matroids ?
نویسندگان
چکیده
This article studies the girth and cogirth problems for connected matroids. The problem of finding the cogirth of a graphic matroid has been intensively studied, but studies on the equivalent problem for a linear matroid or a general matroid have been rarely reported. Based on the duality and connectivity of a matroid, we prove properties associated with the girth and cogirth of a matroid whose contraction or restriction is disconnected. Then, we devise algorithms that find the cogirth of a matroid M from the matroids associated with the direct sum components of the restriction of M . As a result, the problem of finding the (co)girth of a matroid can be decomposed into a set of smaller sub-problems, which helps alleviate the computation. Finally, we implement and demonstrate the application of our algorithms to linear matroids.
منابع مشابه
Computing the minimum cut in hypergraphic matroids
Hypergraphic matroids were de ned by Lorea as generalizations of graphic matroids. We show that the minimum cut (co-girth) of a multiple of a hypergraphic matroid can be computed in polynomial time. It is well-known that the size of the minimum cut (co-girth) of a graph can be computed in polynomial time. For connected graphs, this is equivalent to computing the co-girth of the circuit matroid....
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