Mathematical Sciences - Colloquium
Dr. Shannon Overbay
An n-book is a line in 3-space, called the spine, together with n half-planes, called pages, joined together at the spine. An n-book embedding of a graph G is an embedding of G in an n-book so that each vertex of G lies on the spine and each edge of G lies on a single page so that no two edges cross each other or the spine. The book-thickness of G, or bt(G) is the smallest n such that G admits an n-book embedding.
We will answer some questions about the relationship
between genus and book-thickness originally posed by Bernhart and Kainen.
We will look at bounds for the book-thickness of different families
of graphs, giving an optimal bound for the complete graph. We will demonstrate
a large class of planar graphs of book-thichness two, which includes
X-trees, square grids, and planar bipartite graphs. We will then
consider extensions to generalized books where the pages and spine are
4:10 p.m. in Math 109
Coffee/treats at 3:30 p.m. Math 104 (Lounge)