%0 Journal Article
%@ 0963-5483
%A Sokal, AD
%D 2004
%F discovery:9064
%I CAMBRIDGE UNIV PRESS
%J COMB PROBAB COMPUT
%K GROUND-STATE ENTROPY, MODEL PARTITION-FUNCTIONS, ANTIFERROMAGNETIC POTTS MODELS, PERIODIC BOUNDARY-CONDITIONS, HYPERBOLIC COXETER GROUPS, NONCOMPACT W BOUNDARIES, RANDOM-CLUSTER MEASURES, CYCLIC STRIP GRAPHS, SQUARE-LATTICE, TRIANGULAR-LATTICE
%N 2
%P 221 - 261
%T Chromatic roots are dense in the whole complex plane
%U https://discovery.ucl.ac.uk/id/eprint/9064/
%V 13
%X 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 - l\ < l. The same holds for their dichromatic polynomials (alias Tutte polynomials, alias Potts-model partition functions) Z(G)(q,upsilon) outside the disc \q + upsilon\ < \upsilon\. An immediate corollary is that the chromatic roots of not-necessarily-planar graphs are dense in the whole complex plane. The main technical tool in the proof of these results is the Beraha-Kahane-Weiss theorem oil the limit sets of zeros for certain sequences of analytic functions, for which I give a new and simpler proof.