Identifier

etd-06272011-141751

Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

A graph is almost series-parallel if there is some edge that one can add to the graph and then contract out to leave a series-parallel graph, that is, a graph with no K4-minor. In this dissertation, we find the full list of excluded minors for the class of graphs that are almost series-parallel. We also obtain the corresponding result for the class of graphs such that uncontracting an edge and then deleting the uncontracted edge produces a series-parallel graph.

A notable feature of a 3-connected almost series-parallel graph is that it has two vertices whose removal leaves a tree. This motivates consideration of those graphs for which there are two vertices whose removal is cycle-free. We find the full list of excluded minors for the class of graphs that have a set of at most two vertices whose removal is cycle-free.

Date

2011

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Committee Chair

Oxley, James G.

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