Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounds on the Complex Zeros of (Di)Chromatic Polynomials and Potts-Model
  Partition Functions   I show that there exist universal constants $C(r) < \infty$ such that, for
all loopless graphs $G$ of maximum degree $\le r$, the zeros (real or complex)
of the chromatic polynomial $P_G(q)$ lie in the disc $|q| < C(r)$. Furthermore,
$C(r) \le 7.963906... r$. This result is a corollary of a more general result
on the zeros of the Potts-model partition function $Z_G(q, {v_e})$ in the
complex antiferromagnetic regime $|1 + v_e| \le 1$. The proof is based on a
transformation of the Whitney-Tutte-Fortuin-Kasteleyn representation of $Z_G(q,
{v_e})$ to a polymer gas, followed by verification of the
Dobrushin-Koteck\'y-Preiss condition for nonvanishing of a polymer-model
partition function. I also show that, for all loopless graphs $G$ of
second-largest degree $\le r$, the zeros of $P_G(q)$ lie in the disc $|q| <
C(r) + 1$. Along the way, I give a simple proof of a generalized (multivariate)
Brown-Colbourn conjecture on the zeros of the reliability polynomial for the
special case of series-parallel graphs.

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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: econ