= Hall condition
{c}
{title2=$|N(S)|\geq|S|\quad(S\subseteq L)$}
The <Hall condition> requires enough distinct <neighbours> for \b[every] <subset> of the specified left <vertex set> in a finite <bipartite graph>. Checking the whole left <set> establishes only one inequality. Checking singleton <sets> establishes only that each left <vertex> has positive <degree of a vertex>. Overlapping lists can pass both tests and still fail to admit <matching saturation> of the left side.
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