  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.
