We analyze the optimal behavior of two players who are lost on a planar surface and who want to meet each other in least expected time. They each know the initial distribution of the other’s location, but have no common labeling of points, and so cannot simply go to a location agreed to in advance. They have no compasses, so do not even have a common notion of North. For simplicity, we restrict...

The covering graph of a lattice which is contained in an ordered set with a planar covering graph is itself planar. AMS subject classifications (1980). 06A10

Stern, Manfred. Semimodular lattices: theory and applications. / Manfred Stern. p. cm. – (Encyclopedia of mathematics and its applications ; v. 73) Includes bibliographical references and index.

A subset of vertices a graph is minimal if, within all subsets the same size, its vertex boundary minimal. We give complete, geometric characterization sets for planar integer lattice $X$. Our elucidates structure sets, and we are able to use it obtain several applications. show that neighborhood set characterize uniquely $X$: those which congruent any other size. also classify efficient have m...