Another proof and a generalization of a theorem on N-dimensional stability
β Scribed by Zeheb, E.; Hertz, D.
- Book ID
- 119814284
- Publisher
- IEEE
- Year
- 1984
- Tongue
- English
- Weight
- 190 KB
- Volume
- 72
- Category
- Article
- ISSN
- 0018-9219
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## Abstract For a simple graph of maximum degree Ξ, it is always possible to color the edges with Ξ + 1 colors (Vizing); furthermore, if the set of vertices of maximum degree is independent, Ξ colors suffice (Fournier). In this article, we give a short constructive proof of an extension of these re
We consider the poset P Γ°N ; A 1 ; A 2 ; . . . ; A m Γ consisting of all subsets of a finite set N which do not contain any of the A i 's, where the A i 's are mutually disjoint subsets of N : The elements of P are ordered by inclusion. We show that P belongs to the class of Macaulay posets, i.e. we