On the Pagenumber of k-Trees

A p-page embedding of G is a vertex-ordering π of V (G) (along the “spine” of a book) and an assignment of edges to p half-planes (called “pages”) such that no page contains crossing edges. The pagenumber of G is the least p such that G has a p-page embedding. We disprove a conjecture of Ganley and Heath by showing that for all k ≥ 3, there are k-trees that do not embed in k pages. On the other hand, we present an algorithm that produces k-page embeddings for a special class of k-trees.