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Graphs and Combinatorics

, Volume 29, Issue 4, pp 981–1005 | Cite as

The Planar Slope Number of Planar Partial 3-Trees of Bounded Degree

  • Vít Jelínek
  • Eva Jelínková
  • Jan Kratochvíl
  • Bernard Lidický
  • Marek Tesař
  • Tomáš Vyskočil
Original Paper

Abstract

It is known that every planar graph has a planar embedding where edges are represented by non-crossing straight-line segments. We study the planar slope number, i.e., the minimum number of distinct edge-slopes in such a drawing of a planar graph with maximum degree Δ. We show that the planar slope number of every planar partial 3-tree and also every plane partial 3-tree is at most O(Δ 5). In particular, we answer the question of Dujmović et al. (Comput Geom 38(3):194–212, 2007) whether there is a function f such that plane maximal outerplanar graphs can be drawn using at most f(Δ) slopes.

Keywords

Graph drawing Planar graphs Slopes Planar slope number 

Mathematics Subject Classification

68R10 05C10 05C62 

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Copyright information

© Springer 2012

Authors and Affiliations

  • Vít Jelínek
    • 1
  • Eva Jelínková
    • 1
  • Jan Kratochvíl
    • 1
    • 2
  • Bernard Lidický
    • 1
  • Marek Tesař
    • 1
  • Tomáš Vyskočil
    • 1
    • 2
  1. 1.Department of Applied MathematicsCharles UniversityPragueCzech Republic
  2. 2.Institute for Theoretical Computer ScienceCharles UniversityPragueCzech Republic

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