Genus g Graphs Have Pagenumber O(√ g)

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. We verify a conjecture due to Heath and Istrail which asserts that any graph of genus g has pagenumber O(√ g). This bound is optimal in the worst case. A randomized algorithm to embed a genus g graph in O(√ g) pages is presented.