Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximating the Chromatic Polynomial   Chromatic polynomials are important objects in graph theory and statistical
physics, but as a result of computational difficulties, their study is limited
to graphs that are small, highly structured, or very sparse. We have devised
and implemented two algorithms that approximate the coefficients of the
chromatic polynomial $P(G,x)$, where $P(G,k)$ is the number of proper
$k$-colorings of a graph $G$ for $k\in\mathbb{N}$. Our algorithm is based on a
method of Knuth that estimates the order of a search tree. We compare our
results to the true chromatic polynomial in several known cases, and compare
our error with previous approximation algorithms.

21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int