Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graphs where every k-subset of vertices is an identifying set   Let $G=(V,E)$ be an undirected graph without loops and multiple edges. A
subset $C\subseteq V$ is called \emph{identifying} if for every vertex $x\in V$
the intersection of $C$ and the closed neighbourhood of $x$ is nonempty, and
these intersections are different for different vertices $x$.
  Let $k$ be a positive integer. We will consider graphs where \emph{every}
$k$-subset is identifying. We prove that for every $k>1$ the maximal order of
such a graph is at most $2k-2.$ Constructions attaining the maximal order are
given for infinitely many values of $k.$
  The corresponding problem of $k$-subsets identifying any at most $\ell$
vertices is considered as well.

12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph