UNSOLVED PROBLEMS
in Number Theory, Logic, and Cryptography
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UNSOLVED PROBLEMS in Number Theory, Logic, and Cryptography
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Chromatic Number of the Plane
Suppose you wanted to paint the plane. What is the
minimum number of colors you would need so that all pairs of points exactly 1
unit from each other were a different color? It must be at least four - see
the graph on the left (known as the Moser Spindle), where the lines
show distances of exactly one unit. At least four
colors are needed to ensure that connected nodes are different colors.
At the same time, it is known that seven colors will suffice:
for example the solution on the right, taken from
{2}, where the circles
shown have radius 1 unit.
The
problem is to find a solution to coloring the plane that uses less than 7 colors, or raise the
possible lower bound above 4. For further information,
please see: [1]
http://planetmath.org/?op=getobj&from=objects&name=ChromaticNumberOfASpace [2]
http://www.mathpuzzle.com/chrompln.html [3]
http://maven.smith.edu/~orourke/TOPP/P57.html
* There are currently 0 proposed solutions on the
solutions page. |
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