It is shown that, if an ordered set P contains at most k pairwise disjoint maximal chains, where k is finite, then every finite family of maximal chains in P has a cutset of size at most k. As a corollary of this, we obtain the following Menger-type result that, if in addition, P contains k pairwise
Searching and encoding for infinite ordered sets
โ Scribed by Quentin F. Stout
- Publisher
- Springer
- Year
- 1982
- Tongue
- English
- Weight
- 960 KB
- Volume
- 11
- Category
- Article
- ISSN
- 1573-7640
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Hajnal, A. and N. Sauer, Cut-sets in infinite graphs and partial orders. Discrete Mathematics 117 (1993) 113-125. The set S c V(U) is a cut-set of the vertex v of a graph 9 if v is not adjacent to any vertex in S and, for every maximal clique C of Q, ({v} u S) n C # 0. S is a cut-set of the element
In this paper, we study the notion of arborescent ordered sets, a generalization of the notion of tree-property for cardinals. This notion was already studied previously in the case of directed sets. Our main result gives a geometric condition for an order to be โต0-arborescent.
The Prime Power Conjecture asserts that the order of an affine difference set is an integral power of a prime number. K.T. Arasu and D. Jungnickel have shown that if the order of an affine difference set is even, then the order is either two or four or is divisible by eight. This paper extends this