Perfect precise colorings of plane semiregular tilings

Abstract

A coloring of a planar semiregular tiling {\cal T} is an assignment of a unique color to each tile of {\cal T}. If G is the symmetry group of {\cal T}, the coloring is said to be perfect if every element of G induces a permutation on the finite set of colors. If {\cal T} is k-valent, then a coloring of {\cal T} with k colors is said to be precise if no two tiles of {\cal T} sharing the same vertex have the same color. In this work, perfect precise colorings are obtained for some families of k-valent semiregular tilings in the plane, where k ≤ 6.