Improve the current record of 383/102 for the fractional chromatic number of the plane.Improve the corresponding bound in higher dimensions.Find a 6-chromatic unit-distance graph in the plane.Goal 3: Apply these simpler graphs to inform progress in related areas.Computer assistance was leveraged in to analyze a subgraph of size 397. Goal 2: Reduce (ideally to zero) the reliance on computer assistance for the proof.Goal 1: Find progressively smaller 5-chromatic unit-distance graphs.The Polymath16 project seeks to simplify the graphs used in to establish this lower bound. This is achieved by explicitly locating finite unit distance graphs with chromatic number at least 5. The bounds 4 \leq CNP \leq 7 are classical recently it was shown that CNP \geq 5. The Hadwiger-Nelson problem asks to compute CNP. The Chromatic Number of the Plane (CNP) is the chromatic number of the graph whose vertices are elements of the plane, and two points are connected by an edge if they are a unit distance apart.
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