On the Page Number of Upward Planar Directed Acyclic Graphs

In this paper we study the page number of upward planar directed acyclic graphs. We prove that: (I) 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(k log n), O(2(k))1; (2) every upward planar triangulation G with o(n/log n) 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(root n) does.