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Characterizing posets for which their natural transit functions coincide. (English) Zbl 1316.06003
Summary: 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.

##### MSC:
 06A07 Combinatorics of partially ordered sets 05C38 Paths and cycles 05C12 Distance in graphs
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