Isma Bouchemakh
On the dual K\"{o}nig property of the order-interval hypergraph of a new class of poset
The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 59, 19-27(2005)
MSC:
05C65 Hypergraphs
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 $P$. It is known that ${\cal H}(P)$ has the K\"{o}nig and dual K\"{o}nig properties for the
class of series-parallel posets. Here we introduce a new class
which contains series-parallel posets and for which the dual
K\"{o}nig property is satisfied. For the class of {\large N}-free
posets, again a generalization of series-parallel posets, we give
a counterexample to see that the K\"{o}nig property is not
satisfied.
Keywords: hypergraph, dual K\"{o}nig property
Notes: This work is partially supported by a grant of the DAAD