MT Mathematical Sciences - Colloquium Prof. Nancy Ann Neudauer Department of Mathematics Pacific Lutheran University Representations of Bicircular and Transversal Matroids Matroids are everywhere.
Vector spaces are matroids.
Matroids are useful in situations that are modelled by both graphs and matrices. Bicircular matroids model generalized network flow problems whose algorithms are more efficient than those available for general linear programming codes. In the classical matroid associated with a graph, a set of edges is independent in the matroid if it contains no cycles, and the circuits of the matroid are the single cycles of G . The bicircular matroid is known to be a transversal matroid and thus can be represented by a family of sets, called a presentation. It has been known for some time that the maximal presentation of a transversal matroid is unique.