On the Page Number of Upward Planar Directed Acyclic Graphs

Abstract

In this paper we study the page number of upward planar directed acyclic graphs. We prove that: (1) the page number of any n-vertex upward planar triangulation G whose every maximal 4-connected component has page number k is at most min{O(klogn),O(2^k)}; (2) every upward planar triangulation G with o(n/logn) diameter has o(n) page number; and (3) every upward planar triangulation has a vertex ordering with o(n) page number if and only if every upward planar triangulation whose maximum degree is O(√n) does.