Cover-Decomposition and Polychromatic Numbers

  title={Cover-Decomposition and Polychromatic Numbers},
  author={B{\'e}la Bollob{\'a}s and David Pritchard and Thomas Rothvoss and Alex D. Scott},
  booktitle={SIAM J. Discret. Math.},
A colouring of a hypergraph's vertices is polychromatic if every hyperedge contains at least one vertex of each colour; the polychromatic number is the maximum number of colours in such a colouring. Its dual, the cover-decomposition number, is the maximum number of disjoint hyperedge-covers. In geometric settings, there is extensive work on lower-bounding these numbers in terms of their trivial upper bounds (minimum hyperedge size & degree). Our goal is to get good lower bounds in natural… 
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