A trade-off between page number and page width of book embeddings of graphs (Q1120583)

The author proves that for any integer \(n\geq 3\) there is a family of graphs \(G_{n,k}\), \(k=1,2,..\). such that (1) each \(G_{n,k}\) admits an embedding in a book with n pages, (2) any family of n-page embeddings of the \(G_{n,k}\) has unbounded page width \((=\) maximum number of edges intersecting any perpendicular line to the spine of any page), and (3) there are \((n+1)\)-page embeddings of the \(G_{n,k}'s\) whose page widths are bounded by a constant.