A \emph{wheel} is a graph made of a cycle of length at least~4 together with a vertex that has at least three neighbors in the cycle. We prove that the problem whose instance is a graph G and whose question is "does G contains a wheel as an induced subgraph" is NP-complete. We also settle the complexity of several similar problems.
@article{arxiv.1308.6433,
title = {Detecting wheels},
author = {Emilie Diot and Sébastien Tavenas and Nicolas Trotignon},
journal= {arXiv preprint arXiv:1308.6433},
year = {2014}
}