Characterizing posets for which their natural transit functions coincide

Boštjan Brešar, Manoj Changat, Sandi Klavžar, Joseph Mathews, Antony Mathews, Narasimha-Shenoi Prasanth

Abstract


The standard poset transit function of a poset P is a function TP that assigns to a pair of comparable elements the interval between them, while TP(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.

Keywords


Transit function, ranked poset, underlying graph, geodesic interval, induced-path interval

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DOI: https://doi.org/10.26493/1855-3974.72.9d1

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications