Let G=(V,E) be an undirected graph without loops and multiple edges. A
subset CβV is called \emph{identifying} if for every vertex xβV
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 2kβ2. Constructions attaining the maximal order are
given for infinitely many values of k.
The corresponding problem of k-subsets identifying any at most β
vertices is considered as well.Comment: 21 page