Book embeddings of graphs and a theorem of Whitney

It is shown that the number of pages required for a book embedding of a graph is the maximum of the numbers needed for any of the maximal nonseparable subgraphs and that a plane graph in which every triangle bounds a face has a two-page book embedding. The latter extends a theorem of H. Whitney and gives two-page book embeddings for X-trees and square grids. Key Phrases: Hamiltonian planar graph, book thickness, nicely planar graph, girth, bipartite. This is the full version of Extension of a theorem of Whitney, Appl Math Lett. 20 (2007) 835–837 by the same authors.