Ordered Coloring Grids and Related Graphs

  • Amotz Bar-Noy
  • Panagiotis Cheilaris
  • Michael Lampis
  • Valia Mitsou
  • Stathis Zachos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5869)


We investigate a coloring problem, called ordered coloring, in grids and some other families of grid-like graphs. Ordered coloring (also known as vertex ranking) is related to conflict-free coloring and other traditional coloring problems. Such coloring problems can model (among others) efficient frequency assignments in cellular networks. Our main technical results improve upper and lower bounds for the ordered chromatic number of grids and related graphs. To the best of our knowledge, this is the first attempt to calculate exactly the ordered chromatic number of these graph families.


grid graph ordered coloring vertex ranking conflict-free coloring 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Amotz Bar-Noy
    • 1
    • 2
  • Panagiotis Cheilaris
    • 3
  • Michael Lampis
    • 2
  • Valia Mitsou
    • 2
  • Stathis Zachos
    • 1
    • 2
    • 4
  1. 1.Computer and Information Science Department Brooklyn CollegeCity University of New YorkBrooklynUSA
  2. 2.Doctoral Program in Computer Science The Graduate CenterCity University of New YorkUSA
  3. 3.Alfréd Rényi Institute of MathematicsHungarian Academy of SciencesBudapestHungary
  4. 4.School of Electrical and Computer EngineeringNational Technical University of AthensAthensGreece

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