Related papers: Parameterized Algorithms for Red-Blue Weighted Ver…
A \emph{multipacking} in an undirected graph $G=(V,E)$ is a set $M\subseteq V$ such that for every vertex $v\in V$ and for every integer $r\geq 1$, the ball of radius $ r $ around $ v $ contains at most $r$ vertices of $M$. The…
We study the kernelization complexity of structural parameterizations of the Vertex Cover problem. Here, the goal is to find a polynomial-time preprocessing algorithm that can reduce any instance $(G,k)$ of the Vertex Cover problem to an…
We present the first results on the parameterized complexity of reconfiguration problems, where a reconfiguration version of an optimization problem $Q$ takes as input two feasible solutions $S$ and $T$ and determines if there is a sequence…
The Minimum Vertex Cover problem, a classical NP-complete problem, presents significant challenges for exact solution on large graphs. Fixed-Parameter Tractability (FPT) offers a powerful paradigm to address such problems by exploiting a…
A treedepth decomposition of an undirected graph $G$ is a rooted forest $F$ on the vertex set of $G$ such that every edge $uv\in E(G)$ is in ancestor-descendant relationship in $F$. Given a weight function $w\colon V(G)\rightarrow…
We consider a new Steiner tree problem, called vertex-cover-weighted Steiner tree problem. This problem defines the weight of a Steiner tree as the minimum weight of vertex covers in the tree, and seeks a minimum-weight Steiner tree in a…
Covering problems are fundamental classical problems in optimization, computer science and complexity theory. Typically an input to these problems is a family of sets over a finite universe and the goal is to cover the elements of the…
Treewidth (tw) is an important parameter that, when bounded, yields tractability for many problems. For example, graph problems expressible in Monadic Second Order (MSO) logic and QUANTIFIED SAT or, more generally, QUANTIFIED CSP, are FPT…
In the Properly Colored Spanning Tree problem, we are given an edge-colored undirected graph and the goal is to find a spanning tree in which any two adjacent edges have distinct colors. Since finding such a tree is NP-hard in general,…
We study the Steiner Tree problem, in which a set of terminal vertices needs to be connected in the cheapest possible way in an edge-weighted graph. This problem has been extensively studied from the viewpoint of approximation and also…
In Defective Coloring we are given a graph $G = (V, E)$ and two integers $\chi_d, \Delta^*$ and are asked if we can partition $V$ into $\chi_d$ color classes, so that each class induces a graph of maximum degree $\Delta^*$. We investigate…
For fixed integers $r,\ell \geq 0$, a graph $G$ is called an {\em $(r,\ell)$-graph} if the vertex set $V(G)$ can be partitioned into $r$ independent sets and $\ell$ cliques. The class of $(r, \ell)$ graphs generalizes $r$-colourable graphs…
Suppose the edges of $K_n$ are assigned weights by a weight function $w$. We define the {\em weighted extremal number} \[ \mathrm{ex}(n,w,F):=\max\{w(G)\mid G\subseteq K_n,\text{ and }G\text{ is }F\text{-free}\} \] where $w(G):=\sum_{e\in…
The CONNECTED VERTEX COVER problem asks for a vertex cover in a graph that induces a connected subgraph. The problem is known to be fixed-parameter tractable (FPT), and is unlikely to have a polynomial sized kernel (under complexity…
For a given graph $G$, a depth-first search (DFS) tree $T$ of $G$ is an $r$-rooted spanning tree such that every edge of $G$ is either an edge of $T$ or is between a \textit{descendant} and an \textit{ancestor} in $T$. A graph $G$ together…
In this paper, we develop a new parameterized algorithm for the {\sc Independent Feedback Vertex Set} (IFVS) problem. Given a graph $G=(V,E)$, the goal of the problem is to determine whether there exists a vertex subset $F\subseteq V$ such…
In this paper, we study the Target Set Selection problem from a parameterized complexity perspective. Here for a given graph and a threshold for each vertex, the task is to find a set of vertices (called a target set) which activates the…
We investigate the complexity of counting trees, forests and bases of matroids from a parameterized point of view. It turns out that the problems of computing the number of trees and forests with $k$ edges are $\# W[1]$-hard when…
We investigate the parameterized complexity of the following edge coloring problem motivated by the problem of channel assignment in wireless networks. For an integer q>1 and a graph G, the goal is to find a coloring of the edges of G with…
A connected graph has a $(k,\ell)$-cover if each of its edges is contained in at least $\ell$ cliques of order $k$. Motivated by recent advances in extremal combinatorics and the literature on edge modification problems, we study the…