Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A tree-decomposed transfer matrix for computing exact Potts model
  partition functions for arbitrary graphs, with applications to planar graph
  colourings   Combining tree decomposition and transfer matrix techniques provides a very
general algorithm for computing exact partition functions of statistical models
defined on arbitrary graphs. The algorithm is particularly efficient in the
case of planar graphs. We illustrate it by computing the Potts model partition
functions and chromatic polynomials (the number of proper vertex colourings
using Q colours) for large samples of random planar graphs with up to N=100
vertices. In the latter case, our algorithm yields a sub-exponential average
running time of ~ exp(1.516 sqrt(N)), a substantial improvement over the
exponential running time ~ exp(0.245 N) provided by the hitherto best known
algorithm. We study the statistics of chromatic roots of random planar graphs
in some detail, comparing the findings with results for finite pieces of a
regular lattice.

33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th