Let M be a triangulation of the 2-sphere, with k vertices. Let P(M, n) be its chromatic polynomial with respect to vertex-colorings. Then| P (M, 1 + τ) | ≤ τ5 - kwhere τ is the "golden ratio" (1 + sqrt(5)) / 2. This result is offered as a theoretical explanation of the empirical observation that P(M, n) tends to have a zero near n=1+τ (see ). © 1970 Academic Press, Inc.
Tutte, W. T. (1970). On chromatic polynomials and the golden ratio. Journal of Combinatorial Theory, 9(3), 289–296. https://doi.org/10.1016/S0021-9800(70)80067-9