We study the parameterized complexity of various classic vertex-deletion problems such as
Odd cycle transversal, Vertex planarization, and Chordal vertex deletion under hybrid …

A graph G contains a graph H as an induced minor if H can be obtained from G by vertex
deletions and edge contractions. The class of H-induced-minor-free graphs generalizes the …

Given a graph G and a vertex set X, the annotated treewidth tw (G, X) of X in G is the
maximum treewidth of an X-rooted minor of G, ie, a minor H where the model of each vertex …

Let G be a minor-closed graph class and let 𝐺 be an 𝑛-vertex graph. We say that 𝐺 is a 𝑘-
apex of G if 𝐺 contains a set 𝑆 of at most 𝑘 vertices such that 𝐺\𝑆 belongs to G. Our first …

The exploration of graph width parameters, spanning both graph theory and algebraic
frameworks, has captured substantial attention. Among these, branch width has distinctly …

Given a graph $ G $ and an integer $ k $, Max Min FVS asks whether there exists a minimal
set of vertices of size at least $ k $ whose deletion destroys all cycles. We present several …

For a fixed graph H, the H-IS-Deletion problem asks, given a graph G, for the minimum size
of a set S⊆ V (G) such that G∖ S excludes H as an induced subgraph. We are interested in …

The disjoint paths logic, FOL+ DP, is an extension of First-Order Logic (FOL) with the extra
atomic predicate dp k (x 1, y 1,…, xk, yk), expressing the existence of internally vertex …

Let G be a graph class. We say that a graph G is a k-apex of G if G contains a set S of at most
k vertices such that G⧵ S belongs to G. We prove that if G is minor-closed, then there is an …

The Cut & Count technique and the rank-based approach have lead to single-exponential
FPT algorithms parameterized by treewidth, that is, running in time $2^{O (tw)} n^{O (1)} …