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Density of Chromatic Roots in Minor-Closed Graph Families
Published online by Cambridge University Press: 22 April 2018
Abstract
We prove that the roots of the chromatic polynomials of planar graphs are dense in the interval between 32/27 and 4, except possibly in a small interval around τ + 2 where τ is the golden ratio. This interval arises due to a classical result of Tutte, which states that the chromatic polynomial of every planar graph takes a positive value at τ + 2. Our results lead us to conjecture that τ + 2 is the only such number less than 4.
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- Copyright © Cambridge University Press 2018
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Research supported by ERC Advanced Grant GRACOL, project number 320812.
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