Abstract

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), letf: 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 avertexvareonasingle page. This result generalises that of Malitz [J. Algorithms 17 (1)

Citations