MathNet 2022-part-01 — 197 problems (EN–VI) Question 152

Let $n$ be a positive integer. We call a graph $G$ $n$-good if among any $n$ vertices of $G$ there exist two vertices connected by an edge. Find the least positive integer $N$ such that for any $n$-good connected graph $G$ with $N$ vertices there exists a cycle $C$ with the property:
After deleting all edges of the cycle $C$ the graph $G$ remains connected.