Coloring planar homothets and three-dimensional hypergraphs

@article{Cardinal2011ColoringPH,
  title={Coloring planar homothets and three-dimensional hypergraphs},
  author={Jean Cardinal and Matias Korman},
  journal={Comput. Geom.},
  year={2011},
  volume={46},
  pages={1027-1035}
}
  • Jean Cardinal, Matias Korman
  • Published in Comput. Geom. 2011
  • Mathematics, Computer Science
  • We prove that every finite set of homothetic copies of a given convex body in the plane can be colored with four colors so that any point covered by at least two copies is covered by two copies with distinct colors. This generalizes a previous result from Smorodinsky (SIAM J. Disc. Math. 2007). Then we show that for any k>=2, every three-dimensional hypergraph can be colored with 6(k-1) colors so that every hyperedge e contains min{|e|,k} vertices with mutually distinct colors. This refines a… CONTINUE READING

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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 16 REFERENCES

    Generalized Delaunay Graphs with respect to any Convex Set are Plane Graphs

    VIEW 4 EXCERPTS
    HIGHLY INFLUENTIAL

    Choosability in geometric hypergraphs

    VIEW 10 EXCERPTS
    HIGHLY INFLUENTIAL

    Conflict-Free Coloring Made Stronger

    VIEW 10 EXCERPTS
    HIGHLY INFLUENTIAL

    Coloring Geometric Range Spaces

    VIEW 1 EXCERPT

    Decomposing Coverings and the Planar Sensor Cover Problem

    VIEW 1 EXCERPT

    On Structural and Graph Theoretic Properties of Higher Order Delaunay Graphs

    VIEW 1 EXCERPT

    Decomposition of multiple coverings into many parts

    VIEW 1 EXCERPT

    On the chromatic number of some geometric hypergraphs

    VIEW 2 EXCERPTS

    Conflict-Free Coloring of Points and Simple Regions in the Plane

    VIEW 1 EXCERPT