A Counting of the minimal realizations of the posets of dimension two

The posets of dimension 2 are those posets whose minimal realizations have two elements, that is, which may be obtained as the intersection of two of their linear extensions. Gallai's decomposition of a poset allows for a simple formula to count the number of the distinct minimal realizations of the posets of dimension 2. As an easy consequence, the characterization of M. El-Zahar and of N.W. Sauer of the posets of dimension 2, with an unique minimal realization, is obtained. Mathematics Subject Classi cations (1991): Key words: Counting Dimension Directed Graphs Gallai's Partition Indecomposable Posets Realization.

• Type: Journal
• Year: 2006
• Where: ARSCOM
• Authors: Pierre Ille, Jean-Xavier Rampon
• Keywords: ARSCOM 2006, Dimension, Distinct Minimal Realizations, Minimal Realization