Rivera Omana, Fernanda2022-09-232022-09-232022-09-232022-09-16http://hdl.handle.net/10012/18783The objective of this thesis is to bound the number of points a $U_{2,\ell+2}$- and $M(K_{k+1})$-minor-free matroid has. We first prove that a sufficiently large matroid will contain a structure called a tower. We then use towers to find a complete minor in a matroid with no $U_{2,\ell+2}$-minor.enmatroidclique minorsgraph theoryMaster Thesis