On The Density Of Binary Matroids Without A Given Minor
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On the Density of Binary Matroids Without a Given Minor
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 classes. We will answer this question by finding the eventual growth rate function of the class of matroids with no $\PG(t,2)$-minor, for any $t\ge 2$. Our main tool will be the matroid minors structure theory of Geelen, Gerards, and Whittle, and much of this thesis will be devoted to frame templates, the notion of structure in that theory.
Excluding a Line from Complex-Representable Matroids
Author: James Geelen
language: en
Publisher: American Mathematical Society
Release Date: 2025-01-08
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Graph Structure Theory
Author: Neil Robertson
language: en
Publisher: American Mathematical Soc.
Release Date: 1993-06-14
This volume contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Graph Minors, held at the University of Washington in Seattle in the summer of 1991. Among the topics covered are: algorithms on tree-structured graphs, well-quasi-ordering, logic, infinite graphs, disjoint path problems, surface embeddings, knot theory, graph polynomials, matroid theory, and combinatorial optimization.