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R. Ganian, F. Klute, S. Ordyniak:
"On Structural Parameterizations of the Bounded-Degree Vertex Deletion Problem";
in: "Proceedings of the 35th Symposium on Theoretical Aspects of Computer Science", 35th Symposium on Theoretical Aspects of Computer Science, Cean, 2018, ISBN: 978-3-95977-062-0, 1 - 14.

We study the parameterized complexity of the Bounded-Degree Vertex Deletion problem (BDD),
where the aim is to find a maximum induced subgraph whose maximum degree is below a given
degree bound. Our focus lies on parameters that measure the structural properties of the input
instance. We first show that the problem is W[1]-hard parameterized by a wide range of fairly
restrictive structural parameters such as the feedback vertex set number, pathwidth, treedepth,
and even the size of a minimum vertex deletion set into graphs of pathwidth and treedepth at
most three. We thereby resolve the main open question stated in Betzler, Bredereck, Niedermeier
and Uhlmann (2012) concerning the complexity of BDD parameterized by the feedback vertex
set number. On the positive side, we obtain fixed-parameter algorithms for the problem with
respect to the decompositional parameter treecut width and a novel problem-specific parameter
called the core fracture number.

https://publik.tuwien.ac.at/files/publik_276184.pdf