Adds Proposition 1.13: the number of non-equivalent proper 4-vertex-
colorings of a tire graph T (mod S_4) equals the number of non-
equivalent proper 3-edge-colorings of its partial tire dual D(T) (mod
S_3). The map is the classical Tait XOR construction: identifying
the four colors with Z_2 x Z_2, each edge of T receives an edge color
equal to the XOR of its endpoint colors, which lies in the three
nonzero elements of Z_2 x Z_2 -- giving the corresponding edge of
D(T) a 3-edge-color. Annular triangles of T, encoded as degree-3
vertices d_f of D(T), supply the three-distinct-colors constraint.
Adds Remark 1.14 explaining the analogy with Tait's classical
correspondence.
Adds Tait 1880 bibitem (Proceedings of the Royal Society of Edinburgh,
vol. 10).
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis
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