Dynamics of Transversal Matroids
Hin Lon Lao
Abstract
We propose a way of generating matroids by randomly picking indicator vectors, and since we will see that it mostly gives uniform matroids, which are transversal, we then look at randomly generated transversal matroids. In both models we also investigate threshold phenomena of certain monotone increasing properties. Non-monotone properties of transversal matroids will also be investigated. Moreover, we are going to see how to spot circuits of a transversal matroid from its bipartite graph presentation. In the last Chapter, we have a survey of the characterization of transversal matroids that admit acyclic bipartite presentations. We will also investigate when we can simplify a presentation for a transversal matroid.
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