The Maximum k-Differential Coloring Problem

  • Michael A. Bekos
  • Michael Kaufmann
  • Stephen Kobourov
  • Sankar Veeramoni
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8939)


Given an n-vertex graph G and two positive integers d,k ∈ ℕ, the (d,kn)-differential coloring problem asks for a coloring of the vertices of G (if one exists) with distinct numbers from 1 to kn (treated as colors), such that the minimum difference between the two colors of any adjacent vertices is at least d. While it was known that the problem of determining whether a general graph is (2,n)-differential colorable is NP-complete, our main contribution is a complete characterization of bipartite, planar and outerplanar graphs that admit (2,n)-differential colorings. For practical reasons, we also consider color ranges larger than n, i.e., k > 1. We show that it is NP-complete to determine whether a graph admits a (3,2n)-differential coloring. The same negative result holds for the (\(\lfloor2n/3\rfloor,2n\))-differential coloring problem, even in the case where the input graph is planar.


Bipartite Graph Planar Graph Color Difference Chromatic Number Memetic Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Michael A. Bekos
    • 1
  • Michael Kaufmann
    • 1
  • Stephen Kobourov
    • 2
  • Sankar Veeramoni
    • 2
  1. 1.Wilhelm-Schickard-Institut für InformatikUniversität TübingenGermany
  2. 2.Department of Computer ScienceUniversity of ArizonaTucsonUSA

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