Related papers: Parameterized Complexity and Approximability of Di…
For a graph (undirected, directed, or mixed), a cycle-factor is a collection of vertex-disjoint cycles covering the entire vertex set. Cycle-factors subject to parity constraints arise naturally in the study of structural graph theory and…
Given an undirected graph $G$ and an integer $k$, the Secluded $\Pi$-Subgraph problem asks you to find a maximum size induced subgraph that satisfies a property $\Pi$ and has at most $k$ neighbors in the rest of the graph. This problem has…
A weighted (directed) graph is a (directed) graph with integer weights assigned to its vertices and edges. The weight of a subgraph is the sum of weights of vertices and edges in the subgraph. The problem of determining the largest order…
In $d$-Scattered Set we are given an (edge-weighted) graph and are asked to select at least $k$ vertices, so that the distance between any pair is at least $d$, thus generalizing Independent Set. We provide upper and lower bounds on the…
We show fixed-parameter tractability of the Directed Multicut problem with three terminal pairs (with a randomized algorithm). This problem, given a directed graph $G$, pairs of vertices (called terminals) $(s_1,t_1)$, $(s_2,t_2)$, and…
We study computationally-hard fundamental motion planning problems where the goal is to translate $k$ axis-aligned rectangular robots from their initial positions to their final positions without collision, and with the minimum number of…
We show that the dominating set problem parameterized by solution size is fixed-parameter tractable (FPT) in graphs that do not contain the claw (K(1,3)), the complete bipartite graph on four vertices where the two parts have one and three…
Given a graph with edge costs and vertex profits and given a budget B, the Orienteering Problem asks for a walk of cost at most B of maximum profit. Additionally, each profit may be given with a time window within it can be collected by the…
In this paper we study a maximization version of the classical Edge Dominating Set (EDS) problem, namely, the Upper EDS problem, in the realm of Parameterized Complexity. In this problem, given an undirected graph $G$, a positive integer…
In the Rectangle Stabbing problem, input is a set ${\cal R}$ of axis-parallel rectangles and a set ${\cal L}$ of axis parallel lines in the plane. The task is to find a minimum size set ${\cal L}^* \subseteq {\cal L}$ such that for every…
This paper is devoted to the distributed complexity of finding an approximation of the maximum cut in graphs. A classical algorithm consists in letting each vertex choose its side of the cut uniformly at random. This does not require any…
Given two points in the plane, a set of obstacles defined by closed curves, and an integer $k$, does there exist a path between the two designated points intersecting at most $k$ of the obstacles? This is a fundamental and well-studied…
In the vertex connectivity augmentation problem, we are given an undirected $n$-vertex graph $G$, a set of links $L \subseteq \binom{V(G)}{2} \setminus E(G)$, and integers $\lambda$ and $k$. The task is to insert at most $k$ links from $L$…
We investigate the parameterized complexity of the graph editing problem called Editing to a Graph with a Given Degree Sequence, where the aim is to obtain a graph with a given degree sequence \sigma by at most k vertex or edge deletions…
A circle graph is the intersection graph of a set of chords in a circle. Keil [Discrete Applied Mathematics, 42(1):51-63, 1993] proved that Dominating Set, Connected Dominating Set, and Total Dominating Set are NP-complete in circle graphs.…
In the Dominated Cluster Deletion problem, we are given an undirected graph $G$ and integers $k$ and $d$ and the question is to decide whether there exists a set of at most $k$ vertices whose removal results in a graph in which each…
For the Odd Cycle Transversal problem, the task is to find a small set $S$ of vertices in a graph that intersects every cycle of odd length. The Subset Odd Cycle Transversal problem requires S to intersect only those odd cycles that include…
We prove the existence of a computable function $f\colon\mathbb{N}\to\mathbb{N}$ such that for every integer $k$ and every digraph $D$ either contains a collection $\mathcal{C}$ of $k$ directed cycles of even length such that no vertex of…
In the Disjoint Paths problem, one is given a graph with a set of $k$ vertex pairs $(s_i,t_i)$ and the task is to connect each $s_i$ to $t_i$ with a path, so that the $k$ paths are pairwise disjoint. In the optimization variant, Max…
We prove that there exists a function $f:\mathbb{N}\rightarrow \mathbb{R}$ such that every directed graph $G$ contains either $k$ directed odd cycles where every vertex of $G$ is contained in at most two of them, or a set of at most $f(k)$…