Elsevier

Discrete Mathematics

Volume 145, Issues 1–3, 13 October 1995, Pages 321-327
Discrete Mathematics

Note
Trees as semilattices

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Abstract

We study semilattices whose diagrams are trees. First, we characterize them as semilattices whose convex subsemilattices form a convex geometry, or, equivalently, the closure induced by convex subsemilattices is antiexchange. Then we give lattice theoretic and two graph theoretic characterizations of atomistic semilattices with tree diagrams.

Cited by (0)

1

Supported in part by NSF Grant IRI-90-04137 and AT&T Doctoral Fellowship.

2

On leave from the International Institute of Earthquake Prediction Theory and Mathematical Geophysics, Moscow, Russia.

Copyright © 1995 Published by Elsevier B.V.