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$\DeclareMathOperator\cl{cl}$The cyclic edge connectivity $\cl(G)$ is the size of a smallest cyclic edge cut, i.e., a smallest edge cut $F$ such that $G-F$ has two connected components, each of which ...

It is known that a graph $G=(V,E)$ with $n$ nodes and min cut $k$, must have at least $\frac{1}{2}nk$ edges. Are there any tighter bounds or expectations I can place on $|E|$ if I assume that $G$ ...