Dichotomy for Coloring of Dart Graphs

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


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.


Constant Time Linear Time Common Neighbor Free Graph Central Vertex 
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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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