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.
Work partially supported by the Italian Ministry of Research, grant RBIP06BZW8, FIRB project “Advanced tracking system in intermodal freight transportation”, by the Swiss National Science Foundation 200021-125287/1, by the ESF project 10-EuroGIGA-OP-003 “Graph Drawings and Representations”, and by the MIUR of Italy, project AlgoDEEP 2008TFBWL4.
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Frati, F., Fulek, R., Ruiz-Vargas, A.J. (2012). On the Page Number of Upward Planar Directed Acyclic Graphs. In: van Kreveld, M., Speckmann, B. (eds) Graph Drawing. GD 2011. Lecture Notes in Computer Science, vol 7034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25878-7_37
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