Extension of a theorem of Whitney

It is shown that every planar graph with no separating triangles is a subgraph of a Hamiltonian planar graph; that is, Whitney’s theorem holds without the assumption of a triangulation. Key words. Hamiltonian planar graph, book thickness, separating triangle. 1 Main result For k a positive integer, let Bk be the union of k closed half-planes (the pages) intersecting in a line L (the spine) which is the boundary of each of the pages. A k-page book embedding of a graph G = (V, E) is an embedding of G into Bk with vertices mapped to the spine and with edges intersecting the spine only at their endpoints [14, p. 97]. The book thickness (also called “pagenumber”) of G is the least number of pages in which G has a book embedding. A graph G has book thickness at most 2 if and only if G is a subgraph of a planar Hamiltonian graph [4]. Book thickness has been used as a model for complexity in computer science (e.g., [6], [9]), traffic flow [15], and RNA folding [12]; relations to other ...

• Type: Journal
• Year: 2007
• Where: APPML
• Authors: Paul C. Kainen, Shannon Overbay
• Keywords: APPML 2007, Book Thickness, Hamiltonian Planar Graph, Planar Graph