TITLE: Bipartiteness criterion
QUESTION [6 upvotes]: A graph is bipartite if and only if it does not contain odd cycles. Is there a similar criterion for hypergraphs? (A hypergraph is called bipartite if its vertices can be colored in two colors so that no hyperedge is monochromatic.)
My guess is that the answer is "no" but, maybe, there are results in this direction I am not aware of. Thanks!

REPLY [3 votes]: In "matching theory", by Lovasz and Plummer, I found the following page, which may be helpful: