Cubic Graphs Have Bounded Slope Parameter

  • Balázs Keszegh
  • János Pach
  • Dömötör Pálvölgyi
  • Géza Tóth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5417)


We show that every finite connected graph G with maximum degree three and with at least one vertex of degree smaller than three has a straight-line drawing in the plane satisfying the following conditions. No three vertices are collinear, and a pair of vertices form an edge in G if and only if the segment connecting them is parallel to one of the sides of a previously fixed regular pentagon. It is also proved that every finite graph with maximum degree three permits a straight-line drawing with the above properties using only at most seven different edge slopes.


Maximum Degree Complete Graph Slope Parameter Basic Slope Regular Pentagon 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Balázs Keszegh
    • 1
    • 5
  • János Pach
    • 2
    • 4
    • 5
  • Dömötör Pálvölgyi
    • 3
    • 4
  • Géza Tóth
    • 5
  1. 1.Central European UniversityBudapestHungary
  2. 2.City College, CUNYNew YorkUSA
  3. 3.Eötvös UniversityBudapestHungary
  4. 4.Ecole Polytechnique Fédérale de LausanneSwitzerland
  5. 5.A. Rényi Institute of MathematicsBudapestHungary

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