Abstract
A hypergraph H is (i) Totally balanced if it does not contain a special cycle, (ii) Binary if it is closed under intersection and every hyperedge has at most two predecessors (for inclusion order). We show in this paper that a hypergraph H is totally balanced if and only if it can be embedded into a binary hypergraph H′; H′ is said to be a binary extension of H. We give an efficient algorithm which, given a totally balanced hypergraph H, produces a minimal binary extension Ĥ of H; in addition, if H is a hierarchy or an interval hypergraph, then so is Ĥ.
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