Vertex deletion parameterized by elimination distance and even less

We study the parameterized complexity of various classic vertex-deletion problems such as Odd cycle transversal, Vertex planarization, and Chordal vertex deletion under hybrid parameterizations. Existing FPT algorithms for these problems either focus on the parameterization by solution size, detecting solutions of size k in time f(k) · nO(1), or width parameterizations, finding arbitrarily large optimal solutions in time f(w) · nO(1) for some width measure w like treewidth. We unify these lines of research by presenting FPT algorithms for parameterizations that can simultaneously be arbitrarily much smaller than the solution size and the treewidth.