On the uniformity of the closed-set lattice of a tree (Q1076680)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On the uniformity of the closed-set lattice of a tree |
scientific article; zbMATH DE number 3954946
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the uniformity of the closed-set lattice of a tree |
scientific article; zbMATH DE number 3954946 |
Statements
On the uniformity of the closed-set lattice of a tree (English)
0 references
1986
0 references
Denote by \(\ell^*(L)\) and \(\ell_*(L)\) 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 \(\ell *(L)<k<\ell^*(L)\) there exists in L a maximal chain of length k. In this paper, 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.
0 references
upper length
0 references
lower length
0 references
finite lattice
0 references
maximal chain
0 references
tree
0 references
