Let G(V,E) be an undirected graph with n vertices and m edges such that G has two
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Let G(V,E) be an undirected graph with n vertices and m edges such that G has two vertices s and t where the shortest path from s to t has length strictly more than n/2. Then, prove that there must be a vertex w ∈ V {s,t} such that every path from s to t must pass through w. Furthermore, assuming that G is given to you in the adjacency-list representation along with vertices s and t, design an O(n + m) time algorithm to output such a vertex w. 4. Let G(V.E) be an undirected graph with n vertices and m edges such that G has two vertices s and t where the shortest path from s to t has length strictly more than n/2. Then, prove that there must be a vertex w e V{s,t} such that every path from s to t must pass through w. Furthermore, assuming that G is given to you in the adjacency-list representation along with vertices s and t, design an O(n + m) time algorithm to output such a vertex w.
Related Book For
Introduction to Algorithms
ISBN: 978-0262033848
3rd edition
Authors: Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest
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