Title page for ETD etd-0709103-163907


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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