Let P be an ordered set. P is said to have the finite cutset property if for every x in P there is a finite set F of elements which are noncomparable to x such that every maximal chain in P meets {x} t.J F. It is well known that this property is equivalent to the space of maximal chains of P being c
The finite cutset property
β Scribed by J.-M. Brochet
- Publisher
- John Wiley and Sons
- Year
- 1993
- Tongue
- English
- Weight
- 388 KB
- Volume
- 39
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
A cutset of H is a subset of βͺ H which meets every element of H. H has the finite cutset property if every cutset of H contains a finite one. We study this notion, and in particular how it is related to the compactness of H for the natural topology. MSC: 04A20, 54D30.
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Let G be a finite group, and let Cay(G, S) be a Cayley digraph of G. If, for all T β G, Cay(G, S) βΌ = Cay(G, T ) implies S Ξ± = T for some Ξ± β Aut(G), then Cay(G, S) is called a CI-graph of G. For a group G, if all Cayley digraphs of valency m are CI-graphs, then G is said to have the m-DCI property;