Browsing Mathematics (Faculty of) by Supervisor "Nelson, Peter"
Now showing items 1-4 of 4
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Counting Pentagons in Triangle-free Binary Matroids
(University of Waterloo, 2020-07-30)A rank-n binary matroid is a spanning subset E of F₂ⁿ\{0}, a triangle is a set of three elements from E which sum to zero, and the density of a rank-n binary matroid is |E|/2ⁿ. We begin by giving a new exposition of a ... -
Induced Binary Submatroids
(University of Waterloo, 2021-07-21)The notion of induced subgraphs is extensively studied in graph theory. An example is the famous Gy\'{a}rf\'{a}s-Sumner conjecture, which asserts that given a tree $T$ and a clique $K$, there exists a constant $c$ such ... -
On The Density of Binary Matroids Without a Given Minor
(University of Waterloo, 2016-12-21)This thesis is motivated by the following question: how many elements can a simple binary matroid with no $\PG(t,2)$-minor have? This is a natural analogue of questions asked about the density of graphs in minor-closed ... -
Quadratically Dense Matroids
(University of Waterloo, 2020-07-08)This thesis is concerned with finding the maximum density of rank-$n$ matroids in a minor-closed class. The extremal function of a non-empty minor-closed class $\mathcal M$ of matroids which excludes a rank-2 uniform ...