Sets of points determining only acute angles and some related colouring problems.
Electronic Journal of Combinatorics , 13(1),
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We present both probabilistic and constructive lower bounds on the maximum size of a set of points such that every angle determined by three points in is acute, considering especially the case . These results improve upon a probabilistic lower bound of Erdős and Füredi. We also present lower bounds for some generalisations of the acute angles problem, considering especially some problems concerning colourings of sets of integers.
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