Characterizing posets for which their natural transit functions coincide
Boštjan Brešar, Manoj Changat, Sandi Klavžar, Joseph Mathews, Antony Mathews, Prasanth G. Narasimha-Shenoi · Ars Mathematica Contemporanea · 2009
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.