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seen Nov 7 '13 at 15:36

Nov
6
awarded  Scholar
Nov
6
accepted Achieving the largest possible minimum spacing between vertices of the same color in an integer lattice
Nov
5
comment Achieving the largest possible minimum spacing between vertices of the same color in an integer lattice
I wonder if it's possible to come up with a lowerbound for the best one can do? BTW, I'll +1 you as soon as I have the requisite reputation.
Nov
5
comment Achieving the largest possible minimum spacing between vertices of the same color in an integer lattice
Wouldn't this be an easier instance than asking for the chromatic number of the plane since we restrict ourselves to vertices at defined locations in a lattice?
Nov
5
comment Achieving the largest possible minimum spacing between vertices of the same color in an integer lattice
@BenBarber Thank you - those are some very promising leads.
Nov
5
comment Achieving the largest possible minimum spacing between vertices of the same color in an integer lattice
@BenBarber I am speaking of a Euclidean distance rather than a edge-wise distance, if that makes sense. Imagine, for example, that vertices of the same color repulse one-another as a function of their pairwise Euclidean distance, and we wish to color the vertices to minimize any such repulsive forces. After doing so with $k$ colors (as best we can) what is the minimum distance between vertices of the same color?
Nov
5
awarded  Student
Nov
5
asked Achieving the largest possible minimum spacing between vertices of the same color in an integer lattice