Identifier
etd-03162015-155318
Degree
Doctor of Philosophy (PhD)
Department
Mathematics
Document Type
Dissertation
Abstract
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.
Date
2015
Document Availability at the Time of Submission
Release the entire work immediately for access worldwide.
Recommended Citation
Ferguson, Adam Beau, "Excluding Two Minors of the Petersen Graph" (2015). LSU Doctoral Dissertations. 63.
https://repository.lsu.edu/gradschool_dissertations/63
Committee Chair
Ding, Guoli
DOI
10.31390/gradschool_dissertations.63