Unformatted text preview: u to v or from v to u , or both ( u and v may lie on a cycle). Show that G is semiconnected if and only if the DAG formed by G ’s strongly connected components has a unique topologically sorted order, i.e. there is a unique way to order the DAG vertices v 1 , v 2 , . . . , v n such that any edge ( v i , v j ) satisﬁes i < j . Hint: Let ˜ G denote the DAG of strongly connected components of G . Show that G is semiconnected if and only if ˜ G has the following property: If v i and v i +1 are consecutive vertices in a topological sort of ˜ G , then the edge ( v i , v i +1 ) exists in ˜ G ....
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 Spring '02
 HENZINGER
 Algorithms, Topology, TA, Directed acyclic graph, Strongly connected component, Vazirani

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