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On the uniformity of the closed-set lattice of a tree

โœ Scribed by K.M. Koh; K.S. Poh

Publisher
Elsevier Science
Year
1986
Tongue
English
Weight
578 KB
Volume
61
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

Denote by e*(L) and ~,(L) respectively the upper length and lower length of a finite lattice L. The lattice L is said to be uniform if for each integer k with e,(L) < k < ยข*(L) there exists in L a maximal chain of length k. It is shown that the closed-set lattice of a finite graph G is uniform if G is a tree. The result is not necessarily true if G is not a tree.

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