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 …

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 …

In M. Grohe, S. Kreutzer, and S. Siebertz, J. ACM, 64 (2017), 17 it was shown that nowhere
dense classes of graphs admit sparse neighborhood covers of small degree. We show that a …

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 …

In a social network, the strength of relationships between users can significantly affect the
stability of the network. In this paper, we use the k-truss model to measure the stability of a …

For α>1, an α-approximate (bi) kernel is a polynomial-time algorithm that takes as input an
instance (I,k) of a problem Q and outputs an instance (I',k') (of a problem Q') of size bounded …

Classes with bounded rankwidth are MSO-transductions of trees and classes with bounded
linear rankwidth are MSO-transductions of paths. These results show a strong link between …

We prove that for every class of graphs ℒ which is nowhere dense, as defined by Nešetřil
and Ossona de Mendez [28, 29], and for every first order formula φ (x, y), whenever one …

In 9 it was shown that nowhere dense classes of graphs admit sparse neighbourhood
covers of small degree. We show that a monotone graph class admits sparse …