Routing sets in the integer lattice
A set of vertices S in a graph G is a routing set if it ensures some kind of connectivity between all pairs of vertices outside of S. Additional constraints may apply; a connected dominating set, for instance, is a special case of a routing set. We determine the size of a minimum routing set in subgraphs of the integer lattice, as well as (asymptotically) for the lattice itself.
05c70