
COMMENTS

This counting problem is related to the wellknown problem of finding the "chromatic number of the plane, X(R^2)."
The existence of a simple, connected, unitdistance graph that is ncolorable, 5<=n<=7, will raise the lower bound on X(R^2) from 4, the current lower bound, to n. The upper bound is 7, so should a 7colorable, simple, connected, unitdistance graph be found, the chromatic number of the plane problem will be solved.  Matthew McAndrews, Feb 21 2016
