Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
Selected Problems On Matroid Minors, Jesse Taylor
Selected Problems On Matroid Minors, Jesse Taylor
LSU Doctoral Dissertations
This dissertation begins with an introduction to matroids and graphs. In the first chapter, we develop matroid and graph theory definitions and preliminary results sufficient to discuss the problems presented in the later chapters. These topics include duality, connectivity, matroid minors, and Cunningham and Edmonds's tree decomposition for connected matroids. One of the most well-known excluded-minor results in matroid theory is Tutte's characterization of binary matroids. The class of binary matroids is one of the most widely studied classes of matroids, and its members have many attractive qualities. This motivates the study of matroid classes that are close to being …
On Matroid And Polymatroid Connectivity, Dennis Wayne Hall Ii
On Matroid And Polymatroid Connectivity, Dennis Wayne Hall Ii
LSU Doctoral Dissertations
Matroids were introduced in 1935 by Hassler Whitney to provide a way to abstractly capture the dependence properties common to graphs and matrices. One important class of matroids arises by taking as objects some finite collection of one-dimensional subspaces of a vector space. If, instead, one takes as objects some finite collection of subspaces of dimensions at most k in a vector space, one gets an example of a k-polymatroid.
Connectivity is a pivotal topic of study in the endeavor to understand the structure of matroids and polymatroids. In this dissertation, we study the notion of connectivity from several …