A note on fragile graphs

Guantao Chen, Xingxing Yu
2002 Discrete Mathematics  
In this note, we show that every graph on n vertices and at most 2n − 4 edges contains a vertex-cut S which is also an independent set of G. The result is best possible and answers a question proposed by Caro in the a rmative.
doi:10.1016/s0012-365x(01)00226-6 fatcat:rplyxzqqdrdhzfcqprgrsr46ke