Related papers: A cubic vertex kernel for Diamond-free Edge Deleti…

In an edge modification problem, we are asked to modify at most $k$ edges to a given graph to make the graph satisfy a certain property. Depending on the operations allowed, we have the completion problems and the edge deletion problems. A…

In this work, we study the Biclique-Free Vertex Deletion problem: Given a graph $G$ and integers $k$ and $i \le j$, find a set of at most $k$ vertices that intersects every (not necessarily induced) biclique $K_{i, j}$ in $G$. This is a…

The diamond is the graph obtained by removing an edge from the complete graph on 4 vertices. A graph is ($P_6$, diamond)-free if it contains no induced subgraph isomorphic to a six-vertex path or a diamond. In this paper we show that the…

The pathwidth of a graph is a measure of how path-like the graph is. Given a graph G and an integer k, the problem of finding whether there exist at most k vertices in G whose deletion results in a graph of pathwidth at most one is NP-…

Given a graph $G$ and an integer $k$, the $H$-free Edge Deletion problem asks whether there exists a set of at most $k$ edges of $G$ whose deletion makes $G$ free of induced copies of $H$. Significant attention has been given to the…

Vertex deletion to hereditary graph class is well-studied in parameterized complexity. Vertex deletion to the scattered graph classes has gained attention in recent years. In this paper, we consider (Proper-Interval, Tree)-Vertex Deletion,…

In this paper we study the kernelization of the $d$-Path Vertex Cover ($d$-PVC) problem. Given a graph $G$, the problem requires finding whether there exists a set of at most $k$ vertices whose removal from $G$ results in a graph that does…

It is known that the problem of deleting at most k vertices to obtain a proper interval graph (Proper Interval Vertex Deletion) is fixed parameter tractable. However, whether the problem admits a polynomial kernel or not was open. Here, we…

Given a graph $G$ and an integer $k$, the $H$-free Edge Editing problem is to find whether there exists at most $k$ pairs of vertices in $G$ such that changing the adjacency of the pairs in $G$ results in a graph without any induced copy of…

A graph is distance-hereditary if for any pair of vertices, their distance in every connected induced subgraph containing both vertices is the same as their distance in the original graph. The Distance-Hereditary Vertex Deletion problem…

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 main result is that a polynomial kernel for $k$-Dominating Set on…

The Treewidth-2 Vertex Deletion problem asks whether a set of at most $t$ vertices can be removed from a graph, such that the resulting graph has treewidth at most two. A graph has treewidth at most two if and only if it does not contain a…

A knot $K$ in a directed graph $D$ is a strongly connected component of size at least two such that there is no arc $(u,v)$ with $u \in V(K)$ and $v\notin V(K)$. Given a directed graph $D=(V,E)$, we study Knot-Free Vertex Deletion (KFVD),…

Suppose $\mathcal{F}$ is a finite family of graphs. We consider the following meta-problem, called $\mathcal{F}$-Immersion Deletion: given a graph $G$ and integer $k$, decide whether the deletion of at most $k$ edges of $G$ can result in a…

We study the parameterized and kernelization complexity of the s-Club Cluster Edge Deletion problem, a distance-bounded generalization of Cluster Edge Deletion. Given a graph G = (V, E) and integers k and s, the goal is to delete at most k…

The $3$-colorability problem is a well-known NP-complete problem and it remains NP-complete for $(claw, diamond, K_4)$-free graphs. Recently, $3$-colorability has been also considered for $(claw, N_{1,1,1})$-free graphs. Here, a generalised…

Subdividing an edge $uv$ in a graph replaces it by a path $u w v$ with one new vertex. For a graph $H$, the \textsc{$H$-free Subdivision} problem asks whether, given a graph $G$ and an integer $k$, one can destroy all induced copies of $H$…

The unit interval vertex deletion problem asks for a set of at most $k$ vertices whose deletion from an $n$-vertex graph makes it a unit interval graph. We develop an $O(k^4)$-vertex kernel for the problem, significantly improving the…

The Colouring problem is that of deciding, given a graph $G$ and an integer $k$, whether $G$ admits a (proper) $k$-colouring. For all graphs $H$ up to five vertices, we classify the computational complexity of Colouring for…

For a graph $H$, the $H$-free Edge Deletion problem asks whether there exist at most $k$ edges whose deletion from the input graph $G$ results in a graph without any induced copy of $H$. $H$-free Edge Completion and $H$-free Edge Editing…