Walter Morris

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Coloring copoints of a planar point set
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**Abstract:**
To a set of *n* points in the plane, one can associate a graph that has
less than *n*^{2 vertices and has the property that
k-cliques in the graph correspond to vertex sets of convex k-gons
in the planar point set. We prove an upper bound of 2k-1 on
the size of a planar point set for which the graph has chromatic number
k, matching the bound conjectured by Szekeres for the clique number.
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