Excluding Two Minors of the Petersen Graph

In this dissertation, we begin with a brief survey of the Petersen graph and its role in graph theory. We will then develop an alternative decomposition to clique sums for 3-connected graphs, called T-sums. This decomposition will be used in Chapter 2 to completely characterize those graphs which have no P_3 minor, where P_3 is a graph with 7 vertices, 12 edges, and is isomorphic to the graph created by contracting three edges of a perfect matching of the Petersen Graph. In Chapter 3, we determine the structure of any large internally 4-connected graph which has no P_2 minor, where P_2 is a graph on 8 vertices, 13 edges, and is isomorphic to the graph created by contracting two edges of a perfect matching of the Petersen Graph.

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Applied Mathematics

Grantor

Mathematics

Year dc:date.available

2015

Author dc:creator

• Ferguson, Adam Beau

• Petersen
• Minor exclusion

Statement dc:rights

• unrestricted
• Release the entire work immediately for access worldwide.

Identifier

etd-03162015-155318
https://repository.lsu.edu/gradschool_dissertations/63

OAI identifier oai:identifier

oai:repository.lsu.edu:gradschool_dissertations-1062