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    Every Large Point Set contains Many Collinear Points or an Empty Pentagon

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    We prove the following generalised empty pentagon theorem: for every integer 2\ell \geq 2, every sufficiently large set of points in the plane contains \ell collinear points or an empty pentagon. As an application, we settle the next open case of the "big line or big clique" conjecture of K\'ara, P\'or, and Wood [\emph{Discrete Comput. Geom.} 34(3):497--506, 2005]
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