Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dichotomy Theorems for Homomorphism Polynomials of Graph Classes   In this paper, we will show dichotomy theorems for the computation of
polynomials corresponding to evaluation of graph homomorphisms in Valiant's
model. We are given a fixed graph $H$ and want to find all graphs, from some
graph class, homomorphic to this $H$. These graphs will be encoded by a family
of polynomials.
  We give dichotomies for the polynomials for cycles, cliques, trees,
outerplanar graphs, planar graphs and graphs of bounded genus.

32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
2
The categories of this paper are: math
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph