Discrete Ordered Sets whose Covering Graphs are Median
- 1 May 1984
- journal article
- Published by JSTOR in Proceedings of the American Mathematical Society
- Vol. 91 (1) , 6-8
- https://doi.org/10.2307/2045257
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.Keywords
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