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math.CO2010
Cover-Decomposition and Polychromatic Numbers
Béla Bollobás, David Pritchard, Thomas Rothvoß +1
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…
math.CO2010
Diameter Bounds for Planar Graphs
Radoslav Fulek, Filip Morić, David Pritchard
The inverse degree of a graph is the sum of the reciprocals of the degrees of its vertices. We prove that in any connected planar graph, the diameter is at most 5/2 times the inver…