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On Selected Subclasses Of Matroids, Tara Elizabeth Fife
On Selected Subclasses Of Matroids, Tara Elizabeth Fife
LSU Doctoral Dissertations
Matroids were introduced by Whitney to provide an abstract notion of independence.
In this work, after giving a brief survey of matroid theory, we describe structural results for various classes of matroids. A connected matroid $M$ is unbreakable if, for each of its flats $F$, the matroid $M/F$ is connected%or, equivalently, if $M^*$ has no two skew circuits. . Pfeil showed that a simple graphic matroid $M(G)$ is unbreakable exactly when $G$ is either a cycle or a complete graph. We extend this result to describe which graphs are the underlying graphs of unbreakable frame matroids. A laminar family is …