Let G be a connected graph of order n = 4 and let k be an integer with 2 ≤ k ≤ n − 2. Prove that if G is not k-connected, then G contains a vertex-cut U with |U| = k − 1 and if it is not k-edge-connected, then G contains an edge-cut X with |X| = k − 1
Let G be a connected graph of order n = 4 and let k be an integer with 2 ≤ k ≤ n − 2. Prove that if G is not k-connected, then G contains a vertex-cut U with |U| = k − 1 and if it is not k-edge-connected, then G contains an edge-cut X with |X| = k − 1
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 80EQ
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Let G be a connected graph of order n = 4 and let k be an integer with 2 ≤ k ≤ n − 2. Prove that if G is not k-connected, then G contains a vertex-cut U with |U| = k − 1 and if it is not k-edge-connected, then G contains an edge-cut X with |X| = k − 1
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