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Full-Text Articles in Physical Sciences and Mathematics
Excluded Minors For Nearly-Paving Matroids, Vanessa Natalie Vega
Excluded Minors For Nearly-Paving Matroids, Vanessa Natalie Vega
Electronic Theses, Projects, and Dissertations
Matroids capture an abstract notion of independence that generalizes linear independence in linear algebra, edge independence in graph theory, as well as algebraic independence. Given a particular property of matroids, all the matroids possessing that property form a matroid class. A common research theme in matroid theory is to characterize matroid classes so that, given a matroid M, it is possible to determine whether or not M belongs to a given class. An excluded minor of a minor-closed class is a matroid N that is, in a sense, minimal with respect to not being in the minor-closed class. An attractive …
Exploring Matroid Minors, Jonathan Lara Tejeda
Exploring Matroid Minors, Jonathan Lara Tejeda
Electronic Theses, Projects, and Dissertations
Matroids are discrete mathematical objects that generalize important concepts of independence arising in other areas of mathematics. There are many different important classes of matroids and a frequent problem in matroid theory is to determine whether or not a given matroid belongs to a certain class of matroids. For special classes of matroids that are minor-closed, this question is commonly answered by determining a complete list of matroids that are not in the class but have the property that each of their proper minors is in the class; that is, minor-minimal matroids that are not in the minor-closed class. These …