Fixing Improper Colorings of Graphs

  • Konstanty Junosza-Szaniawski
  • Mathieu Liedloff
  • Paweł Rzążewski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8939)


In this paper we consider a variation of a recoloring problem, called the r-Color-Fixing. Let us have some non-proper r-coloring ϕ of a graph G. We investigate the problem of finding a proper r-coloring of G, which is “the most similar” to ϕ, i.e. the number k of vertices that have to be recolored is minimum possible. We observe that the problem is NP-complete for any r ≥ 3, but is Fixed Parameter Tractable (FPT), when parametrized by the number of allowed transformations k. We provide an \(\mathcal{O}^*(2^n)\) algorithm for the problem (for any fixed r) and a linear algorithm for graphs with bounded treewidth. Finally, we investigate the fixing number of a graph G. It is the maximum possible distance (in the number of transformations) between some non-proper coloring of G and a proper one.


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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Konstanty Junosza-Szaniawski
    • 1
  • Mathieu Liedloff
    • 2
  • Paweł Rzążewski
    • 1
  1. 1.Faculty of Mathematics and Information ScienceWarsaw University of TechnologyWarszawaPoland
  2. 2.INSA Centre Val de Loire, LIFOUniversité d’OrléansOrléansFrance

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