Graphs and Combinatorics

, Volume 29, Issue 4, pp 981–1005

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

DOI: 10.1007/s00373-012-1157-z

Cite this article as:
Jelínek, V., Jelínková, E., Kratochvíl, J. et al. Graphs and Combinatorics (2013) 29: 981. doi:10.1007/s00373-012-1157-z

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(Δ5). 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 

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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