Combinatorics-Matroids from Graphs and Graphs from Matroids

Speaker: Deborah Chun, West Virginia University Institute of Technology
Date and time: Tuesday, April 24, 1-2pm
Place: Rome 771
Title:  Matroids from Graphs and Graphs from Matroids
Abstract:
In this talk, we will introduce matroids.  Matroid theory generalizes the idea of independence that can come up in various fields, including graph theory.  Theorems in matroid theory often have corollaries that are theorems in graph theory.  An example of this will be given.

If G is a graph, we can construct a matroid from G in multiple ways.  Two matroids from graphs, the cycle matroid and the bicircular matroid, will be defined.  Similarly, if M is a matroid, we can construct multiple graphs from M.  We will define the basis exchange graph of a matroid.  We will give some results for these objects.