This article presents an algorithm which computes the dimension of an arbitrary ลฝ . finite poset partial order set . This algorithm is based on the chromatic number of a graph instead of the classical approach based on the chromatic number of some hypergraph. The relation between both approaches is
A note on the dimension of a poset
โ Scribed by E. C. Milner; M. Pouzet
- Publisher
- Springer Netherlands
- Year
- 1990
- Tongue
- English
- Weight
- 93 KB
- Volume
- 7
- Category
- Article
- ISSN
- 0167-8094
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โฆ Synopsis
It is shown that the dimension of a poset is the smallest cardinal number I such that there is an embedding of the poset into a strict product of I, linear orders.
๐ SIMILAR VOLUMES
For any poset P let J(P) denote the complete lattice of order ideals in P. J(P) is a contravariant functor in P. Any order-reversing map f: P-+Q can be regarded as an isotone (= order-preserving) map of either P\* into Q or P into Q\*. The induced map of J(Q) to J(P\*) (resp. J(Q\*) into J(P)) will
In [l] Feinberg conjectures that the maximum circular dimension of all graphs having n vertices is attained by a complete partite graph. In this note we show that this is not so. In [l], Feinberg defined the circular dimension of a graph as follows: Given a graph G = (V, E), a collection of functio