On the page number of upward planar directed acyclic graphs

  • Authors:

  • Fabrizio Frati;Radoslav Fulek;Andres J. Ruiz-Vargas

  • Affiliations:

  • School of Basic Sciences, École Polytechnique Fédérale de Lausanne, Switzerland;School of Basic Sciences, École Polytechnique Fédérale de Lausanne, Switzerland;School of Basic Sciences, École Polytechnique Fédérale de Lausanne, Switzerland

  • Venue:
  • GD'11 Proceedings of the 19th international conference on Graph Drawing
  • Year:
  • 2011

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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(2k)}; (2) every upward planar triangulation G with $o(\frac{n}{\log n})$ 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 $O(\sqrt n)$ does.