Identifier

etd-0709103-163907

Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

We use a structural theorem of Robertson and Seymour to show that for every minor-closed class of graphs, other than the class of all graphs, there is a number k such that every member of the class can be embedded in a book with k pages. Book embeddings of graphs with relation to surfaces, vertex extensions, clique-sums and r-rings are combined into a single book embedding of a graph in the minor-closed class. The effects of subdividing a complete graph and a complete bipartite graph with respect to book thickness are studied. We prove that if n ≥ 3, then the book thickness of Kn is the ceiling of (n/2). We also prove that for each m and B, there exists an integer N such that for all n ≥ ‪N, the book thickness of the graph obtained from subdividing each edge of Kn exactly m times has book thickness at least B. Additionally, there are corresponding theorems for complete bipartite graphs.

Date

2003

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Committee Chair

Bogdan Oporowski

DOI

10.31390/gradschool_dissertations.3734

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