A minimax theorem for chain complete ordered sets
โ Scribed by Henry A. Kierstead
- Publisher
- Springer Netherlands
- Year
- 1988
- Tongue
- English
- Weight
- 513 KB
- Volume
- 5
- Category
- Article
- ISSN
- 0167-8094
No coin nor oath required. For personal study only.
โฆ Synopsis
It is shown that if a chain complete ordered set does not have k+ 1 pairwise disjoint maximal chains for some finite k, then the minimum size of a cutset is equal to the maximum size of a collection of pairwise disjoint maximal chains. This answers a question of Pouzet and Zaguia.
๐ SIMILAR VOLUMES
Let N (n, k) be the set of all n-tuples over the alphabet {0, 1, . . . , k} whose component sum equals . A subset F โ N (n, k) is called a t-intersecting family if every two tuples in F have nonzero entries in at least t common coordinates. We determine the maximum size of a t-intersecting family in
The authors have proved in a recent paper a complete intersection theorem for systems of finite sets. Now we establish such a result for nontrivial-intersection systems (in the sense of Hilton and Milner [Quart.
Polat, N., A minimax theorem for infinite graphs with ideal points, Discrete Mathematics 103 (1992) 57-65. Let d be a family of sets of ends of an infinite graph, having the property that every element of any member of 1 can be separated from the union of all other members by a finite set of vertice