J. Aust. Math. Soc.
77 (2004), 191196

On the chromatic number of plane tilings


Abstract

It is known that
, where
is the number of colours necessary to colour
each point of Euclidean 2space so that no two
points lying distance 1 apart have the same
colour. Any latticesublattice colouring scheme
for must use at least 7 colours to have an excluded
distance. This article shows that at least 6
colours are necessary for an excluded distance
when convex polygonal tiles (all with area
greater than some positive constant) are used as
the colouring base.

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