Spotting Circuits in Bipartite Presentations of Transversal Matroids

Hin Lon Lao, York University

A natural way to present a transversal matroid is by drawing a bipartite graph. We are going to see when given a bipartite presentation of a transversal matroid, how we can spot circuits of the transversal matroid by looking at the bipartite graph. Also, we spot edges which can be removed without affecting the transversal matroid it presents when the corresponding induced subgraphs of circuits intersect in a nice way in the bipartite graph. Moreover, we can apply our result to to make certain communication networks simpler.