4-Coloring H-Free Graphs When H Is Small

  • Petr A. Golovach
  • Daniël Paulusma
  • Jian Song
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7147)


The k-Coloring problem is to test whether a graph can be colored with at most k colors such that no two adjacent vertices receive the same color. If a graph G does not contain a graph H as an induced subgraph, then G is called H-free. For any fixed graph H on at most 6 vertices, it is known that 3-Coloring is polynomial-time solvable on H-free graphs whenever H is a linear forest and NP-complete otherwise. By solving the missing case P 2 + P 3, we prove the same result for 4-Coloring provided that H is a fixed graph on at most 5 vertices.


Polynomial Time Disjoint Union Adjacent Vertex Graph Class Perfect Graph 
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 2012

Authors and Affiliations

  • Petr A. Golovach
    • 1
  • Daniël Paulusma
    • 1
  • Jian Song
    • 1
  1. 1.School of Engineering and Computing SciencesDurham University, Science LaboratoriesDurhamUnited Kingdom

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