Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

A series-parallel graph can be built from a single-edge graph by a sequence of series and parallel extensions. The class of such graphs coincides with the class of graphs that do not have the complete graph K4 as a minor. This dissertation considers a class M1 of graphs that are close to being series-parallel. In particular, every member of the class has the property that one can obtain a series-parallel graph by adding a new edge and contracting it out, or by splitting a vertex into two vertices whose neighbor sets partition the neighbor set of the original vertex. The class M1 is minor-closed. The goal of this dissertation is to show that M1 has exactly twelve excluded minors, including K5, the cube, and the octahedron.

Date

12-13-2017

Committee Chair

Oxley, James

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