The formal definition of a k-connected graph $G$ is:
$\nexists x\subseteq V(G)$ with $|x| \le k - 1$ such that $G-x$ is disconnected.
What is the intuition behind this? What does it mean to be 2-connected or 3-connected?
2026-04-11 18:11:12.1775931072
Intuition of a k-connected graph?
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How much connected a graph is? k-connectedness is a measure of connectedness of a graph. Suppose you have a connected graph. Deleting vertices from the graph results deleting its incident edges also. For a given graph $G$, suppose minimum number of vertices you should remove to make its disconnected is $k$. Then, the graph is $k$-connected. Some examples will make it more transparent.
Draw a circle of 5 vertices. Remove one vertex. Is the resultant graph disconnected? To make it disconnected minimum two vertices to be removed. Every circle is 2-connected.
Draw a complete graph. How many vertices do you need to make it disconnected? Measure its connectivity!