Cycle transversals in bounded degree graphs

In this work we consider the problem of finding a minimum C k -transversal (a subset of vertices hitting all the induced chordless cycles with k vertices) in a graph with bounded maximum degree. In particular, we seek for dichotomy results as follows: for a fixed value of k, finding a minimum C k -transversal is polynomial-time solvable if k ⩽ p , and NP-hard otherwise.