The minimum size of a k-connected locally nonforesty graph of order n is determined exactly for k=4, k=2 and k=1, and equals ceil(kn/2) for k at least 5.
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The minimum size of a $k$-connected locally nonforesty graph
The minimum size of a k-connected locally nonforesty graph of order n is determined exactly for k=4, k=2 and k=1, and equals ceil(kn/2) for k at least 5.