Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modular counting of subgraphs: Matchings, matching-splittable graphs,
  and paths   We systematically investigate the complexity of counting subgraph patterns
modulo fixed integers. For example, it is known that the parity of the number
of $k$-matchings can be determined in polynomial time by a simple reduction to
the determinant. We generalize this to an $n^{f(t,s)}$-time algorithm to
compute modulo $2^t$ the number of subgraph occurrences of patterns that are
$s$ vertices away from being matchings. This shows that the known
polynomial-time cases of subgraph detection (Jansen and Marx, SODA 2015) carry
over into the setting of counting modulo $2^t$.
  Complementing our algorithm, we also give a simple and self-contained proof
that counting $k$-matchings modulo odd integers $q$ is Mod_q-W[1]-complete and
prove that counting $k$-paths modulo $2$ is Parity-W[1]-complete, answering an
open question by Bj\"orklund, Dell, and Husfeldt (ICALP 2015).

29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
2
The categories of this paper are: math
17
The categories of this paper are: q-fin