#### 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 K_{n} 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 K_{n} 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.

#### Recommended Citation

Blankenship, Robin Leigh, "Book embeddings of graphs" (2003). *LSU Doctoral Dissertations*. 3734.

https://digitalcommons.lsu.edu/gradschool_dissertations/3734

#### Committee Chair

Bogdan Oporowski