Graphs orientable as distributive lattices
Dwight Duffus, Ivan Rival · Proceedings of the American Mathematical Society · 1983
There are two types of graphs commonly associated with finite (partially) ordered sets: the comparability graph and the covering graph. While the first type has been characterized, only partial descriptions of the second are known. We prove that the covering graphs of distributive lattices are precisely those graphs which are retracts of hypercubes.