NP-Hardness of the $H$-Free Edge-Deletion Problem
For a graph $H$, the $H$-freeness edge-deletion problem is the algorithmic problem of finding, for an input graph $G$, the minimum number of edges of $G$ whose deletion turns $G$ into an $H$-free graph. We show that for every graph $H$ containing a cycle, this problem is NP-hard. This proves a conjecture of Gishboliner...