Characterizations of Some Classes of Graphs That Are Nearly Series-Parallel

Author

Victoria Fontaine, Louisiana State University and Agricultural and Mechanical CollegeFollow

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

Recommended Citation

Fontaine, Victoria, "Characterizations of Some Classes of Graphs That Are Nearly Series-Parallel" (2017). LSU Doctoral Dissertations. 4179.
https://repository.lsu.edu/gradschool_dissertations/4179

Committee Chair

Oxley, James

DOI

10.31390/gradschool_dissertations.4179