Planar Lattice Subsets with Minimal Vertex Boundary
Planar Lattice Subsets with Minimal Vertex Boundary
A subset of vertices of a graph is minimal if, within all subsets of the same size, its vertex boundary is minimal. We give a complete, geometric characterization of minimal sets for the planar integer lattice $X$. Our characterization elucidates the structure of all minimal sets, and we are able …