2 Suppose we can construct a graph with N number of vertices, what’s the minimum number of edges…

2

Suppose we can construct a graph with N number of vertices, what’s the minimum number of edges that graph needs to have so that it can’t have an articulation point? In other words, it needs to be biconnected.

A complete graph obviously doesn’t have any articulation point, but we can still remove some of its edges and it may still not have any. So it seems it can have lesser number of edges than the complete graph. With N vertices, there are a number of ways in which we can construct graph. So this minimum number should satisfy any of those graphs.

Clarification as the title is confusing for users – What is the smallest m (as a function of n) such that every n-vertex graph having at least m edges is necessarily biconnected?

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