Chromatic Roots are Dense in the Whole Complex Plane

  • Authors:

  • Alan D. Sokal

  • Affiliations:

  • Department of Physics, New York University, 4 Washington Place, New York, NY 10003, USA (e-mail: sokal@nyu.edu)

  • Venue:
  • Combinatorics, Probability and Computing
  • Year:
  • 2004

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Abstract

I show that the zeros of the chromatic polynomials $P_G(q)$ for the generalized theta graphs $\Theta^{(s,p)}$ are, taken together, dense in the whole complex plane with the possible exception of the disc $|q-1|