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: (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(k logn), O(2)}; (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. Submitted: January 2013 Accepted: March 2013 Final: April 2013 Published: May 2013 Article type: Regular paper Communicated by: G. Liotta Work partially supported by the Swiss National Science Foundation, grant no. 200021125287/1, and by the ESF project 10-EuroGIGA-OP-003 “Graph Drawings and Representations”. A preliminary version of this paper is to appear at GD ’11 [8]. E-mail addresses: [email protected] (Fabrizio Frati) [email protected] (Radoslav Fulek) [email protected] (Andres J. Ruiz-Vargas) 222 Frati, Fulek, Ruiz-Vargas On the Page Number of Upward Planar DAG