Abstract
We consider a variation on the problem of determining the chromatic number of the Euclidean plane and define the ε-unit distance graph to be the graph whose vertices are the points of E2, in which two points are adjacent whenever their distance is within ε of 1. For certain values of ε we are able to show that the chromatic number is exactly 7. For some smaller values we show the chromatic number is at least 5. We offer a conjecture, with some supporting evidence, that for any ε > 0 the chromatic number is 7.
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Exoo, G. ε-Unit Distance Graphs. Discrete Comput Geom 33, 117–123 (2005). https://doi.org/10.1007/s00454-004-1092-8
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DOI: https://doi.org/10.1007/s00454-004-1092-8