The survey is a comprehensive overview of the developing area of parameterized
algorithms for graph modification problems. It describes state of the art in kernelization …

We introduce the notion of universal obstruction of a graph parameter, with respect to some
quasi-ordering relation. Universal obstructions may serve as compact characterizations of …

Tree-cut width is a graph parameter introduced by Wollan [24] that is an analogue of
treewidth for the immersion order on graphs in the following sense: the tree-cut width of a …

We introduce a novel model-theoretic framework inspired from graph modification and
based on the interplay between model theory and algorithmic graph minors. The core of our …

The $ t $-onion star is the digraph obtained from a star with $2 t $ leaves by replacing every
edge by a triple of arcs, where in $ t $ triples we orient two arcs away from the center, and in …

We introduce the graph theoretical parameter of edge-treewidth. This parameter occurs in a
natural way as the tree-like analogue of cutwidth or, alternatively, as an edge-analogue of …

Let G, H be graphs, and G⁎ H represent a specific graph product of G and H. Define im (G)
as the largest t for which G contains a K t-immersion. Collins, Heenehan, and McDonald …

For a fixed simple digraph $ H $ without isolated vertices, we consider the problem of
deleting arcs from a given tournament to get a digraph which does not contain $ H $ as an …

We present a collection of results in structural graph theory and the theory of parameterized
algorithms, all of which are based upon understanding the structure of graphs disallowed to …

The immersion number of a graph G, denoted im (G), is the largest t such that G has a K t-
immersion. In this note we are interested in determining the immersion number of the m …