Rényi Institute researchers confirm more than 50-year-old conjecture of Paul Erdős

What fraction of the plane can be colored so that two colored points cannot be exactly a unit distance away from each other? This geometric question was formulated by Leo Moser in the early 1960s. According to a conjecture of Paul Erdős, this fraction must be less than ¼. The currently best lower bound of 0.2293 is given by a construction by Hallard Croft dating back to 1967. Several research groups have published partial results on the problem, gradually strengthening the initial upper density estimate of 0.
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