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The order-interval hypergraph of a finite poset and the König property

✍ Scribed by Isma Bouchemakh; Konrad Engel

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
561 KB
Volume
170
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

We study the hypergraph ~(P) whose vertices are the points of a finite poset and whose edges are the maximal intervals in P (i.e. sets of the form I = {v ~ P:p <~ v <<. q}, p minimal, q maximal). We mention resp. show that the problems of the determination of the independence number c~, the point covering number r, the matching number v and the edge covering number p are NP-complete. For interval orders we describe polynomial algorithms and prove the K6nig property (v = 3) and the dual K6nig property (~ = p). Finally we show that the (dual) K6nig property is preserved by product.

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