Document Type
Lecture
Publication Date
11-2-2012
Abstract
A matroid is a mathematical set system that is a common generalization of the concepts of a graph and of a projective geometry. Many important results in combinatorics deal with excluded-minor characterizations of classes of graphs and matroids. One famous example of such a result is Kuratowskis Theorem which states that a graph is planar if and only if it is K5K33free. Guoli Ding and Cheng Liu have characterized many classes of graphs that are H-free for graphs H with fewer than twelve edges. We have extended some of their results to the class of regular 3-connected matroids. Dillon Mayhew and Gordon Royle recently characterized the class of binary internally 4-connected matroids that are prism-free. As an extension of their result, we have determined the structure of the class of binary 3connected matroids that are (prism + e)-free. We will also brie y discuss MACEK, a matroid computing program developed by Petr Hlineny that has proven to be particularly useful in our work in excluded-minor characterizations.
Relational Format
presentation
Recommended Citation
Harville, Kayla Davis, "On Regular and Binary Matroids Without Small Minors" (2012). Combinatorics Seminar. 60.
https://egrove.olemiss.edu/math_combinatorics/60
