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Predecessor Subgraph

$G_{pred} \;=\; (V_{pred}, \;E_{pred})$ is a predecessor subgraph of G if

V_pred = {v $\in$ V $\mid$ pred(v) $\neq$ NIL} $\cup$ {s}

E_pred = {(pred(v), v) $\in$ E $\mid$ v $\in$ V_pred - {s}}

Lemma 23.5 The pred tree generated by BFS results in a predecessor subgraph G_pred which defines a BF tree.

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