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Motions on n-Simplex Graphs with m-value memory

Marc Zucker
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Abstract

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.

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Marc Zucker. 2003-10-01. Motions on n-Simplex Graphs with m-value memory. https://arxiv.org/abs/math/0310015

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