Odd-Cycle-Free Facet Complexes and the König property

Details Odd-Cycle-Free Facet Complexes and the König property Odd-Cycle-Free Facet Complexes and the König property

2007-03-15

arxiv.org/abs/math/0703459v1

Mathematics

Commutative Algebra

12 pages, 11 figures

Scientific paper

We use the definition of a simplicial cycle to define an odd-cycle-free facet complex (hypergraph). These are facet complexes that do not contain any cycles of odd length. We show that besides one class of such facet complexes, all of them satisfy the K\"onig property. This new family of complexes includes the family of balanced hypergraphs, which are known to satisfy the K\"onig property. These facet complexes are, however, not Mengerian; we give an example to demonstrate this fact.

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