TY  - JOUR
AV  - public
Y1  - 2004/03//
SP  - 221 
ID  - discovery9064
PB  - CAMBRIDGE UNIV PRESS
N2  - 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.
KW  - GROUND-STATE ENTROPY
KW  -  MODEL PARTITION-FUNCTIONS
KW  -  ANTIFERROMAGNETIC POTTS MODELS
KW  -  PERIODIC BOUNDARY-CONDITIONS
KW  -  HYPERBOLIC COXETER GROUPS
KW  -  NONCOMPACT W BOUNDARIES
KW  -  RANDOM-CLUSTER MEASURES
KW  -  CYCLIC STRIP GRAPHS
KW  -  SQUARE-LATTICE
KW  -  TRIANGULAR-LATTICE
UR  - https://discovery.ucl.ac.uk/id/eprint/9064/
JF  - COMB PROBAB COMPUT
SN  - 0963-5483
TI  - Chromatic roots are dense in the whole complex plane
A1  - Sokal, AD
EP  -  261
IS  - 2
VL  - 13
ER  -