Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recovering sparse graphs   We construct a fixed parameter algorithm parameterized by d and k that takes
as an input a graph G' obtained from a d-degenerate graph G by complementing on
at most k arbitrary subsets of the vertex set of G and outputs a graph H such
that G and H agree on all but f(d,k) vertices.
  Our work is motivated by the first order model checking in graph classes that
are first order interpretable in classes of sparse graphs. We derive as a
corollary that if G_0 is a graph class with bounded expansion, then the first
order model checking is fixed parameter tractable in the class of all graphs
that can obtained from a graph G from G_0 by complementing on at most k
arbitrary subsets of the vertex set of G; this implies an earlier result that
the first order model checking is fixed parameter tractable in graph classes
interpretable in classes of graphs with bounded maximum degree.

15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio