Related papers: A Quartic Kernel for Pathwidth-One Vertex Deletion

We study the design of fixed-parameter algorithms for problems already known to be solvable in polynomial time. The main motivation is to get more efficient algorithms for problems with unattractive polynomial running times. Here, we focus…

Finding paths in graphs is a fundamental graph-theoretic task. In this work, we we are concerned with finding a path with some constraints on its length and the number of vertices neighboring the path, that is, being outside of and incident…

For a graph $G$ and a parameter $k$, we call a vertex $k$-enabling if it belongs both to a clique of size $k$ and to an independent set of size $k$, and we call it $k$-excluding otherwise. Motivated by issues that arise in secret sharing…

For a graph $G$, a subset $S\subseteq V(G)$ is called a resolving set of $G$ if, for any two vertices $u,v\in V(G)$, there exists a vertex $w\in S$ such that $d(w,u)\neq d(w,v)$. The Metric Dimension problem takes as input a graph $G$ on…

For a set of graphs $\mathcal{H}$, the \textsc{$\mathcal{H}$-free Edge Deletion} problem asks to find whether there exist at most $k$ edges in the input graph whose deletion results in a graph without any induced copy of $H\in\mathcal{H}$.…

Let $n$ be the size of a parameterized problem and $k$ the parameter. We present kernels for Feedback Vertex Set, Path Contraction and Cluster Editing/Deletion whose sizes are all polynomial in $k$ and that are computable in polynomial time…

Motivated by the planarization of 2-layered straight-line drawings, we consider the problem of modifying a graph such that the resulting graph has pathwidth at most 1. The problem Pathwidth-One Vertex Explosion (POVE) asks whether such a…

For a class of graphs $\mathcal{P}$, the Bounded $\mathcal{P}$-Block Vertex Deletion problem asks, given a graph $G$ on $n$ vertices and positive integers $k$ and $d$, whether there is a set $S$ of at most $k$ vertices such that each block…

We study a general class of problems called F-deletion problems. In an F-deletion problem, we are asked whether a subset of at most $k$ vertices can be deleted from a graph $G$ such that the resulting graph does not contain as a minor any…

In the 4-path vertex cover problem, the input is an undirected graph $G$ and an integer $k$. The goal is to decide whether there is a set of vertices $S$ of size at most $k$ such that every path with 4 vertices in $G$ contains at least one…

Given a graph $G=(V,E)$, two vertices $s,t\in V$, and two integers $k,\ell$, the Short Secluded Path problem is to find a simple $s$-$t$-path with at most $k$ vertices and $\ell$ neighbors. We study the parameterized complexity of the…

A set of vertices $W$ in a graph $G$ is called resolving if for any two distinct $x,y\in V(G)$, there is $v\in W$ such that ${\rm dist}_G(v,x)\neq{\rm dist}_G(v,y)$, where ${\rm dist}_G(u,v)$ denotes the length of a shortest path between…

Given a graph $G=(V,E)$, a set $\mathcal{F}$ of forbidden subgraphs, we study $\mathcal{F}$-Free Edge Deletion, where the goal is to remove minimum number of edges such that the resulting graph does not contain any $F\in \mathcal{F}$ as a…

We consider the problem of finding a Hamiltonian path or cycle with precedence constraints in the form of a partial order on the vertex set. We study the complexity for graph width parameters for which the ordinary problems…

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…

A graph is said to be a Konig graph if the size of its maximum matching is equal to the size of its minimum vertex cover. The Konig Edge Deletion problem asks if in a given graph there exists a set of at most k edges whose deletion results…

Given a graph $G$, an integer $k\geq 0$, and a non-negative integral function $f:V(G) \rightarrow \mathcal{N}$, the Vector Domination problem asks whether a set $S$ of vertices, of cardinality $k$ or less, exists in $G$ so that every vertex…

The three-in-a-tree problem asks for an induced tree of the input graph containing three mandatory vertices. In 2006, Chudnovsky and Seymour [Combinatorica, 2010] presented the first polynomial time algorithm for this problem, which has…

The notion of treewidth plays an important role in theoretical and practical studies of graph problems. It has been recognized that, especially in practical environments, when computing the treewidth of a graph it is invaluable to first…

We study the CONNECTED \eta-TREEDEPTH DELETION problem where the input instance is an undireted graph G = (V, E) and an integer k. The objective is to decide if G has a set S \subseteq V(G) of at most k vertices such that G - S has…