In graph theory, a **cut** is a way to partition the vertices of a graph into two disjoint subsets. More formally, given a graph \( G = (V, E) \), a cut is defined by a subset of the vertices \( S \subseteq V \). The cut divides the graph into two parts: one containing the vertices in \( S \) and the other containing the vertices in \( V \setminus S \).
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A cut is a partition of the vertex set. Its size is the number of edges with one endpoint in each part.