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An ideal I in a Noetherian ring R is normally torsion-free ifAss(R/I^t)=Ass(R/I) for all natural numbers t. We develop a technique toinductively study normally torsion-free square-free monomial ideals. Inparticular, we show that if a square-free monomial ideal I is minimally notnormally torsion-free then the least power t such that I^t has embedded primesis bigger than beta_1, where beta_1 is the monomial grade of I, which is equalto the matching number of the hypergraph H(I) associated to I. If in addition Ifails to have the packing property, then embedded primes of I^t do occur whent=beta_1 +1. As an application, we investigate how these results relate to aconjecture of Conforti and Cornu\'ejols.

Embedded Associated Primes of Powers of Square-free Monomial Ideals