Deficiency

Deficiency --- дефицит.

The deficiency [math]\displaystyle{ def({\mathcal A}) }[/math] of a family [math]\displaystyle{ {\mathcal A} }[/math] of hypergraphs is the minimal natural number [math]\displaystyle{ d }[/math] such that the matching width [math]\displaystyle{ mw({\mathcal B}) }[/math] satisfies the condition

[math]\displaystyle{ mw(\cup{\mathcal B}) \geq |{\mathcal B}| - d }[/math]

for every subfamily [math]\displaystyle{ {\mathcal B} }[/math] of [math]\displaystyle{ {\mathcal A} }[/math].