Consider a directed acyclic graph G E). We run DFS on G from a E V. This results in a BFS forest with two trees T1 = (V1, E1) and T = (V2, E2), where a € V1. Prove or disprove the following statements. a There must exist a topological sort O of G in which every v e V½ occurs before every w e Vị.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Consider a directed acyclic graph G = (V,E). We run DFS on G from a e V. This results in a DFS forest with
two trees T1 = (V1, E1 ) and T2 = (V2, E2), where a E Vi. Prove or disprove the following statements.
a There must exist a topological sort O of G in which every v e V½ occurs before every w e Vị.
b There may exist a topological sort O' of G in which every v e V½ occurs after every w e V1.
Transcribed Image Text:Consider a directed acyclic graph G = (V,E). We run DFS on G from a e V. This results in a DFS forest with two trees T1 = (V1, E1 ) and T2 = (V2, E2), where a E Vi. Prove or disprove the following statements. a There must exist a topological sort O of G in which every v e V½ occurs before every w e Vị. b There may exist a topological sort O' of G in which every v e V½ occurs after every w e V1.
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