Date of Award
M.A. in Mathematics
Talmadge James Reid
Stanislaw M. Dziobiak
This thesis considers a Ramsey Theory question for graphs and regular matroids. Specifically, how many elements N are required in a 3-connected graphic or regular matroid to force the existence of certain specified minors in that matroid? This question cannot be answered for an arbitrary collection of specified minors. However, there are results from the literature for which the number N exists for certain collections of minors. We first encode totally unimodular matrix representations of certain matroids. We use the computer program MACEK to investigate this question for certain classes of specified minors.
Horne, Dixie Smith, "Ramsey Theory Using Matroid Minors" (2014). Electronic Theses and Dissertations. 668.