  We introduce the idea of an n-simplex graph and games upon simplicial
complexes. We then define moves on a labeled graph and pose the problem of
whether given two labelings of a graph it is possible to change one into
another via these moves. We then solve the problem for a given class of graphs.
Once having found a solution for a given class of graphs we determine the
number of different solutions that exist. We then use this to find an algorithm
to determine whether a graph is (n+1)-colorable, and in particular, whether it
is 3-colorable.
