Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Parameterised Complexity of Counting Connected Subgraphs and Graph
  Motifs   We introduce a class of parameterised counting problems on graphs, p-#Induced
Subgraph With Property(\Phi), which generalises a number of problems which have
previously been studied. This paper focusses on the case in which \Phi defines
a family of graphs whose edge-minimal elements all have bounded treewidth; this
includes the special case in which \Phi describes the property of being
connected. We show that exactly counting the number of connected induced
k-vertex subgraphs in an n-vertex graph is #W[1]-hard, but on the other hand
there exists an FPTRAS for the problem; more generally, we show that there
exists an FPTRAS for p-#Induced Subgraph With Property(\Phi) whenever \Phi is
monotone and all the minimal graphs satisfying \Phi have bounded treewidth. We
then apply these results to a counting version of the Graph Motif problem.

18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat