#### Filter Results:

#### Publication Year

1977

2010

#### Publication Type

#### Co-author

#### Publication Venue

#### Key Phrases

Learn More

The size of a minimum realizer of a partial order is called the dimension of that partial order. Here we initiate the study of minimal realizers which are not minimum. As an aid to the study of such realizers, we associate to each minimal realizer certain critical digraphs. We characterize all such critical digraphs for the antichain on n elements, and… (More)

The rank (resp. dimension) of a poset P is the cardinality of a largest (resp. smallest) set of linear orders such that its intersection is P and no proper subset has intersectior: P. Dimension has been studied extensively. Rank was introduced recently by Maurer and Rabinovitch in [4], where the rank of antichains was determined. In this paper we develop a… (More)

We consider An extremal problem for directed graphs which is closely related to Tutin's theorem giving the maximum number of edges in a gr;lph on n vertices which does not contain a complete subgraph on m vertices. and edge set {(i. j): 1 s i C j s n]. A subgraph H of T,, is said to be m-locally unipathic when the restriction of H to each m element subset… (More)

- ‹
- 1
- ›