On Structural Parameterizations of the Bounded-Degree Vertex Deletion Problem


This publication doesn't include Institute of Computer Science. It includes Faculty of Informatics. Official publication website can be found on muni.cz.

GANIAN Robert KLUTE Fabian ORDYNIAK Sebastian

Year of publication 2018
Type Article in Proceedings
Conference STACS 2018
MU Faculty or unit

Faculty of Informatics

Doi http://dx.doi.org/10.4230/LIPIcs.STACS.2018.33
Keywords bounded-degree vertex deletion; feedback vertex set; parameterized algorithms; treecut width
Description 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.
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