Characterizing posets for which their natural transit functions coincide

Abstract

The standard poset transit function of a poset P is a function T_P that assigns to a pair of comparable elements the interval between them, while T_P(x,y) = {x,y} for a pair x, y of incomparable elements. Posets in which the standard poset transit function coincides with the shortest-path transit function of its cover-incomparability graph are characterized in three ways, in particular with forbidden subposets.