Centers of sets of pixels

The center of a connected graph G is the set of nodes of G for which the maximum distance to any other node of G is as small as possible. If G is a simply connected set of lattice points (\pixels") with graph structure deened by 4-neighbor adjacency, we show that the center of G is either a 2-by-2 square block, a diagonal staircase, or a (dotted) diagonal line with no gaps. The authors thank Fridrich Sloboda for suggesting the problem, Reinhard Klette for early discussions, and Janice Perrone for her help in preparing this paper.