Graphs where every k-subset of vertices is an identifying set

Sylvain Gravier, Svante Janson, Tero Laihonen, Sanna Ranto
2014 Discrete Mathematics & Theoretical Computer Science  
Combinatorics International audience 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
more » ... 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.
doi:10.46298/dmtcs.1253 fatcat:so2helcfprdrtidgn7gsw5t4su