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* A clutter ''C'' has the '''max flow min cut property''' ('''MFMC property''' for short) if both ''LP(C)'' and its dual have integral optimal solutions if <math>w \in \mathbb{Z}_+^V</math>. Equivalently, if ''LP(C)'' is [[Total dual integrality|TDI]].
* A clutter ''C'' is '''ideal''' if ''LP(C)'' has an integral optimal solution if <math>w \in \mathbb{Z}_+^V</math>. Equivalently, if ''LP(C)'' describes an integer polyhedron.
The '''blocker''' of a clutter is the clutter of inclusionwise minimal transversals. Given a clutter ''C'' and an element <math>v \in V</math>, the '''deletion''' of ''v'' means the restriction of the clutter to <math>V-v</math>, while the '''contraction''' of ''v'' is the clutter on ground set <math>V-v</math> formed by the inclusionwise minimal elements of <math>\{X-v: X \in C\}</math>. A '''minor''' of ''C'' is a clutter obtained by a sequence of deletions and contractions.
A comprehensive description on the topic can be found in Cornuéjols' book <ref>G. Cornuéjols, ''Combinatorial Optimization: Packing and Covering'', [http://integer.tepper.cmu.edu/webpub/notes.ps author link]</ref>. See also the [[Wikipedia:Clutter (mathematics)|Wikipedia article]].
