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Dichotomy for Coloring of Dart Graphs

  • Martin Kochol
  • Riste Škrekovski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6460)

Abstract

We study a (k + 1)-coloring problem in a class of (k,s)-dart graphs, k,s ≥ 2, where each vertex of degree at least k + 2 belongs to a (k,i)-diamond, i ≤ s. We prove that dichotomy holds, that means the problem is either NP-complete (if k < s), or can be solved in linear time (if k ≥ s). In particular, in the latter case we generalize the classical Brooks Theorem, that means we prove that a (k, s)-dart graph, k ≥ max {2,s}, is (k + 1)-colorable unless it contains a component isomorphic to K k + 2.

Keywords

Constant Time Linear Time Common Neighbor Free Graph Central Vertex 
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 2011

Authors and Affiliations

  • Martin Kochol
    • 1
  • Riste Škrekovski
    • 2
  1. 1.MÚ SAVBratislava 1Slovakia
  2. 2.Department of MathematicsUniversity of LjubljanaLjubljanaSlovenia

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