Simple product colorings |
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Authors: | Peter D Johnson |
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Institution: | Department of Mathematics, Auburn University, AL 36849, USA |
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Abstract: | If A is a set colored with m colors, and B is colored with n colors, the coloring of A × B obtained by coloring (a, b) with the pair (color of a, color of b) will be called an m × n simple product coloring (SPC) of A × B. SPC's of Cartesian products of three or more sets are defined analogously. It is shown that there are 2 × 2, and 2 × 2 × 2 SPC's of 2 and 3 which forbid the distance one; that there is no 2k SPC of k forbidding the distance one, for k > 3; and that there is no 2 × 2 SPC of × (√15), and thus none of 2, forbidding the distance 1. |
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