Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Edge colourings and topological graph polynomials   A k-valuation is a special type of edge k-colouring of a medial graph.
Various graph polynomials, such as the Tutte, Penrose, Bollob\'as-Riordan, and
transition polynomials, admit combinatorial interpretations and evaluations as
weighted counts of k-valuations. In this paper, we consider a multivariate
generating function of k-valuations. We show that this is a polynomial in k and
hence defines a graph polynomial. We then show that the resulting polynomial
has several desirable properties, including a recursive
deletion-contraction-type definition, and specialises to the graph polynomials
mentioned above. It also offers an alternative extension of the Penrose
polynomial from plane graphs to graphs in other surfaces.

11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph