We prove that whenever G is a graph from a nowhere dense graph class C, and A is a subset of vertices of G, then the number of subsets of A that are realized as intersections of A with… (More)

Suppose F is a finite family of graphs. We consider the following meta-problem, called FImmersion Deletion: given a graph G and integer k, decide whether the deletion of at most k edges of G can… (More)

For every k ≥ 0, we define Gk as the class of graphs with treedepth at most k, i.e. the class containing every graph G admitting a valid colouring ρ : V (G) → {1, . . . , k} such that every (x,… (More)

The <i>F</i>-M<scp>inor</scp>-F<scp>ree</scp> D<scp>eletion</scp> problem asks, for a fixed set <i>F</i> and an input consisting of a graph <i>G</i> and integer <i>k</i>, whether <i>k</i> vertices… (More)

Cutwidth is one of the classic layout parameters for graphs. It measures how well one can order the vertices of a graph in a linear manner, so that the maximum number of edges between any prefix and… (More)

The immersion relation is a partial ordering relation on graphs that is weaker than the topological minor relation in the sense that if a graph G contains a graph H as a topological minor, then it… (More)

We study the structure of graphs that do not contain the wheel on 5 vertices W4 as an immersion, and show that these graphs can be constructed via 1, 2, and 3-edge-sums from subcubic graphs and… (More)

A graph H is an immersion of a graph G if H can be obtained by some subgraph G after lifting incident edges. We prove that there is a polynomial function f : N×N→ N, such that if H is a connected… (More)