Degree constrained book embeddings

A book embedding of a graph consists of a linear ordering of the vertices along a line in 3-space (the spine), and an assignment of edges to half-planes with the spine as boundary (the pages), so that edges assigned to the same page can be drawn on that page without crossings. Given a graph G= (V ,E), let f :V → N be a function such that 1 f (v) deg(v). We present a Las Vegas algorithm which produces a book embedding of G with O( √|E| · maxv deg(v)/f (v) ) pages, such that at most f (v) edges incident to a vertex v are on a single page. This result generalises that of Malitz [J. Algorithms 17 (1) (1994) 71–84].  2002 Elsevier Science (USA). All rights reserved.