Type of Document	Dissertation
Author	Blankenship, Robin Leigh
Author's Email Address	rblank1@lsu.edu
URN	etd-0709103-163907
Title	Book Embeddings of Graphs
Degree	Doctor of Philosophy (Ph.D.)
Department	Mathematics
Advisory Committee	Advisor Name Title Bogdan Oporowski Committee Chair Frank Neubrander Committee Member James Oxley Committee Member Patrick Gilmer Committee Member Robert Lax Committee Member Doris Carver Dean's Representative
Keywords	representativity apex vertices tree widths
Date of Defense	2003-07-01
Availability	unrestricted
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.
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