A graph is biconnected if every pair of vertices is connected by two disjoint paths. An articulation point in a connected graph is a vertex that would disconnect the graph if it (and its adjacent edges) were removed. Prove that any graph with no articulation points is biconnected. Hint : Given a pair of vertices s and t and a path connecting them, use the fact that none of the vertices on the path are articulation points to construct two disjoint paths connecting s and t.
A graph is biconnected if every pair of vertices is connected by two disjoint paths. An articulation point in a connected graph is a vertex that would disconnect the graph if it (and its adjacent edges) were removed. Prove that any graph with no articulation points is biconnected. Hint : Given a pair of vertices s and t and a path connecting them, use the fact that none of the vertices on the path are articulation points to construct two disjoint paths connecting s and t.
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
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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A graph is biconnected if every pair of vertices is connected
by two disjoint paths. An articulation point in a connected graph is a vertex that would
disconnect the graph if it (and its adjacent edges) were removed. Prove that any graph
with no articulation points is biconnected. Hint : Given a pair of vertices s and t and a
path connecting them, use the fact that none of the vertices on the path are articulation
points to construct two disjoint paths connecting s and t.
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