The subject of graph convexity is well explored in the literature, the so-called interval convexities above all. In this work, we explore the cycle convexity, whose interval function is $I(S) = S \cup \{u \mid G[S \cup \{u\}]$ has a cycle containing $u\}$. In this convexity, we prove that the decision problems associated to the parameters rank and convexity number are in \NP-complete and \W[1]-hard when parameterized by the solution size. We also prove that to determine whether the percolation time of a graph is at least $k$ is \NP-complete, but polynomial for cacti or when $k\leq2$

翻译：图凸性问题是文献中广泛研究的课题，尤其是所谓的区间凸性。本文探讨了循环凸性，其区间函数定义为 $I(S) = S \cup \{u \mid G[S \cup \{u\}]$ 包含一个包含 $u$ 的循环$\}$。在该凸性中，我们证明了与秩和凸性数参数相关的判定问题在参数化解规模下属于\NP-完全和\W[1]-困难。我们还证明了确定图的渗透时间是否至少为 $k$ 是\NP-完全的，但对于仙人掌图或当 $k\leq2$ 时该问题为多项式时间可解。