@inproceedings{Martin2018DisconnectedCI,
title={Disconnected Cuts in Claw-free Graphs},
author={B. Martin and D. Paulusma and E. J. V. Leeuwen},
booktitle={ESA},
year={2018}
}

A disconnected cut of a connected graph is a vertex cut that itself also induces a disconnected subgraph. The decision problem whether a graph has a disconnected cut is called Disconnected Cut. This problem is closely related to several homomorphism and contraction problems, and fits in an extensive line of research on vertex cuts with additional properties. It is known that Disconnected Cut is NP-hard on general graphs, while polynomial-time algorithms are known for several graph classesâ€¦Â Expand