# maximum number of graph min-cuts, when edge-connectivity $c$ is odd

Based on the cactus representation of minimum cuts, it would seem that for a graph with $n$ vertices and edge-connectivity $c$, where $c$ is odd, that the maximum number of min-cuts is something like $n$ or $n-1$. (This is clearly true for $c = 1$).

I just want to confirm that this is correct? Is there are any reference that lays this out clearly?

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