Forbidden minors for 3-connected graphs with no non-splitting 5-configurations

Resource type
Thesis type
(Thesis) M.Sc.
Date created
2012-08-09
Authors/Contributors
Author: Crump, Iain
Abstract
For a set of five edges, a graph splits if one of the associated Dodgson polynomials is equal to zero. A graph G splitting for every set of five edges is a minor-closed property. As such there is a finite set of forbidden minors F such that if a graph H does not contain a minor isomorphic to any graph in F}, then H splits. In this paper we prove that if a graph G is simple, 3-connected, and splits, then G must not contain any minors isomorphic to K5, K3,3, the octahedron, the cube, or a graph that is a single Delta-Y transformation away from the cube. As such this is the set of all simple 3-connected forbidden minors. The complete set of 2-connected or non-simple forbidden minors remains unresolved, though a number have been found.
Document
Identifier
etd7334
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The author granted permission for the file to be printed and for the text to be copied and pasted.
Scholarly level
Supervisor or Senior Supervisor
Thesis advisor: Yeats, Karen
Member of collection
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