Grid Drawings and the Chromatic Number

  • Martin Balko
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7704)


A grid drawing of a graph maps vertices to the grid ℤ d and edges to line segments that avoid grid points representing other vertices. We show that a graph G is q d -colorable, d, q ≥ 2, if and only if there is a grid drawing of G in ℤ d in which no line segment intersects more than q grid points. This strengthens the result of D. Flores Pen̋aloza and F. J. Zaragoza Martinez. Second, we study grid drawings with a bounded number of columns, introducing some new NP-complete problems. Finally, we show that any planar graph has a planar grid drawing where every line segment contains exactly two grid points. This result proves conjectures asked by D. Flores Pen̋aloza and F. J. Zaragoza Martinez.


graph drawings grid graph coloring chromatic number 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Martin Balko
    • 1
  1. 1.Department of Applied Mathematics, Faculty of Mathematics and PhysicsCharles UniversityPraha 1Czech Republic

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