On -unit distance graphs
نویسنده
چکیده
We consider a variation on the problem of determining the chromatic number of the Euclidean plane and define the -unit distance graph to be the graph whose vertices are the points of E, in which two points are adjacent whenever their distance is within of 1. For certain values of we are able to show that the chromatic number is exactly seven. For some smaller values we show the chromatic number is at least five. Computational evidence suggests that for any > 0 the chromatic number may be seven.
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تاریخ انتشار 2003