A graph vertex-subset problem defines which subsets of the vertices of an input graph are
feasible solutions. We view a feasible solution as a set of tokens placed on the vertices of …

Bidimensionality theory appears to be a powerful framework in the development of meta-
algorithmic techniques. It was introduced by Demaine et al.[J. ACM 2005] as a tool to obtain …

We study the existence of polynomial kernels, for parameterized problems without a
polynomial kernel on general graphs, when restricted to graphs of bounded twin-width. Our …

A graph vertex-subset problem defines which subsets of the vertices of an input graph are
feasible solutions. We view a feasible solution as a set of tokens placed on the vertices of …

We prove that whenever $ G $ is a graph from a nowhere dense graph class $\mathcal {C}
$, and $ A $ is a subset of vertices of $ G $, then the number of subsets of $ A $ that are …

We prove that graph problems with finite integer index have linear kernels on graphs of
bounded expansion when parameterized by the size of a modulator to constant-treedepth …

The generalised colouring numbers col r (G) and wcol r (G) were introduced by Kierstead
and Yang as a generalisation of the usual colouring number, and have since then found …

The notion of structural sparsity is discussed, and its relation to thenowhere
dense/somewhere dense'dichotomy introduced by the authors for classes of graphs is …

Nowhere dense classes of graphs [21, 22] are very general classes of uniformly sparse
graphs with several seemingly unrelated characterisations. From an algorithmic perspective …

A vertex-subset graph problem Q defines which subsets of the vertices of an input graph are
feasible solutions. A reconfiguration variant of a vertex-subset problem asks, given two …