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Proceedings of the American Mathematical Society

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Discrete ordered sets whose covering graphs are median


Author: Hans-J. Bandelt
Journal: Proc. Amer. Math. Soc. 91 (1984), 6-8
MSC: Primary 06A10; Secondary 05C75, 06A12
DOI: https://doi.org/10.1090/S0002-9939-1984-0735552-6
MathSciNet review: 735552
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Abstract: As is well known the covering graph (= Hasse diagram) of any median semilattice is a median graph, and every median graph is the covering graph of some median semilattice. The purpose of this note is to prove that an ordered set is a median semilattice whenever (i) no interval contains an infinite chain, (ii) each pair of elements is bounded below, and (iii) the covering graph is median.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0735552-6
Keywords: Discrete ordered set, covering graph, median semilattice, distributive lattice, median graph
Article copyright: © Copyright 1984 American Mathematical Society