Efficient Deterministic Algorithms for Embedding Graphs on Books

We derive deterministic polynomial time algorithms for book embedding of a graph G = (V; E), jV j = n and jEj = m. In particular, we present the rst deterministic polynomial time algorithm to embed any bipartite graph in O(p m) pages. We then use this algorithm to embed, in polynomial time, any graph G in O(p (G) m) pages, where (G) is the largest minimum degree over all subgraphs of G. Our algorithms are obtained by derandomizing the probabilistic proofs.