Isolation of Cycles - Borg, Peter (Graphs and combinatorics, 2020)
For any graph G , let ι c ( G ) denote the size of a smallest set D of vertices of G such that the graph obtained from G by deleting the closed neighbourhood of D contains no cycle. We prove that if G is a connected n -vertex graph that is not a triangle, then ι c ( G ) ≤ n / 4 . We also show that the bound is sharp. Consequently, this settles a problem of Caro and Hansberg.