Unique-Maximum and Conflict-Free Coloring for Hypergraphs and Tree Graphs

  • Panagiotis Cheilaris
  • Balázs Keszegh
  • Dömötör Pálvölgyi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7147)


We investigate the relationship between two kinds of vertex colorings of hypergraphs: unique-maximum colorings and conflict-free colorings. In a unique-maximum coloring, the colors are ordered, and in every hyperedge of the hypergraph the maximum color in the hyperedge occurs in only one vertex of the hyperedge. In a conflict-free coloring, in every hyperedge of the hypergraph there exists a color in the hyperedge that occurs in only one vertex of the hyperedge. We define corresponding unique-maximum and conflict-free chromatic numbers and investigate their relationship in arbitrary hypergraphs. Then, we concentrate on hypergraphs that are induced by simple paths in tree graphs.


Chromatic Number Parity Vector Tree Graph Central Edge Vertex Coloring 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Panagiotis Cheilaris
    • 1
  • Balázs Keszegh
    • 2
  • Dömötör Pálvölgyi
    • 3
  1. 1.Center for Advanced Studies in MathematicsBen-Gurion UniversityBe’er ShevaIsrael
  2. 2.Alfréd Rényi Institute of MathematicsBudapestHungary
  3. 3.Eötvös UniversityBudapestHungary

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