Excluded Minor Results in Matroids
On Monday, November 14, 2011, the York College Tensor Scholars Program featured a talk by Dr. Sandra Kingan from the Department of Mathematics at Brooklyn College, CUNY titled Excluded Minor Results in Matroids.
The excluded minor results on which she focused are some of the most celebrated results in graph and matroid structure theory. For a given class of matroids with a specified structure, a minimal excluded minor is a matroid that is not in the class though every single-element deletion and contraction is in the class.
Such matroids are minimal obstructions for membership in the class. For example, the complete graph on five vertices and the complete bipartite graph with three vertices in each class are the minimal obstructions to planarity in graphs.
Several classes of matroids such as binary, ternary, and quaternary matroids can be characterized in terms of their minimal obstructions. Dr. Kingan’s talk was an interesting introduction to matroids for many in attendance.