**Isma Bouchemakh**

**On the K\"{o}nig and the dual K\"{o}nig property of order-interval hypergraphs of series-parallel posets**

**The paper is published:**
Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. [56], [3]-[8]([2002])

**MSC:**- 05C65 Hypergraphs
- 06A07 Combinatorics of partially ordered sets

**Abstract:** Let $P$ be a finite poset. We consider the hypergraph ${\cal H}(P)$

whose vertices are the elements of $P$ and whose edges are the maximal

intervals of $P.$ We prove the K\"{o}nig and the dual K\"{o}nig property of $%

{\cal H}(P)$ for the class of series-parallel posets.

**Keywords:** *Hypergraphs, Combinatorics of partially ordered sets*