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Facet complexes and simplicial cycles were introduced to help study the interplay between graph theoretical and algebraic properties of hypergraphs. 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 Konig property. This new family of complexes includes the family of balanced hypergraphs, which are known to satisfy the Konig property. These odd-cycle-free facet complexes are, however, not necessarily Mengerian. Copyright © 2011 Rocky Mountain Mathematics Consortium

Odd-cycle-free facet complexes and the König property