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Let C be a uniform clutter and let I = I ( C ) be its edge ideal. We prove that if C satisfies the packing property (resp. max-flow min-cut property), then there is a uniform Cohen-Macaulay clutter C 1 satisfying the packing property (resp. max-flow min-cut property) such that C is a minor of C 1 . For arbitrary edge ideals of clutters we prove that the normality property is closed under parallelizations. Then we show some applications to edge ideals and clutters which are related to a conjecture of Conforti and Cornu´ejols and to max-flow min-cut problems. 2000 Mathematics Subject Classification: Primary 13H10; Secondary 13F20, 13B22, 52B20.

Cohen-Macaulay clutters with combinatorial optimization properties and parallelizations of normal edge ideals