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 drawingPlanar graphsSlopesPlanar slope number

Mathematics Subject Classification

68R1005C1005C62

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