In spite of the fact that there are only two classes of three-qubit genuine entanglement: W and GHZ, we show that there are three-qubit genuinely entangled states which can not be detected neither by W nor by GHZ entanglement witnesses.
@article{arxiv.quant-ph/0506035,
title = {How to fool the GHZ and W witnesses},
author = {D. Cavalcanti and M. O. Terra Cunha},
journal= {arXiv preprint arXiv:quant-ph/0506035},
year = {2007}
}