Abstract
A book embedding of a graph consists of a linear ordering of the vertices along the spine of a book and an assignment of edges to pages so that edges residing on the same page do not intersect. The minimum number of pages in which a graph can be embedded is its pagenumber. The main results of this paper: (1) any graph with E edges has pagenumber O(√E); (2) there is a d-regular N-vertex graph with pagenumber Ω(√ d N 1/2-1/ d ). The first bound is tight in the worst case; the second bound is tight when d > log N. Both results are dramatic improvements over previously known bounds.
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