Prove if G is k-connected graph then removing any k edges from G will yield a graph with at most 2 connected components. I have no idea where to start even though I know it is true. I have tried it on many graphs and the proposition works. Please help me. Thank you
2026-04-01 18:17:21.1775067441
Removing k edges from G will yield a graph with at most 2 connected components
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Pick $k-1$ of your edges. For each of these edges, make sure that one adjacent vertex is removed (including all its incident edges). Hence, all of the $k-1$ edges are also removed. By $k$-connectivity, your graph is still connected after removing these at most $k-1$ vertices. Now observe that removing the last edge can increase the amount of connected components at most by 1.