Related papers: Algorithms and Hardness for Geodetic Set on Tree-l…

For a digraph $G$, a set $F\subseteq V(G)$ is said to be a feedback vertex set (FVS) if $G-F$ is acyclic. The problem of finding a smallest FVS is NP-hard. We present a matrix scaling technique for finding feedback vertex sets in…

Let $G(V,E)$ be a simple, undirected and connected graph. A dominating set $S \subseteq V(G)$ is called a $2$-\textit{secure dominating set} ($2$-SDS) in $G$, if for every pair of distinct vertices $u_1,u_2 \in V(G)$ there exists a pair of…

Let $G=(V,E)$ and $H$ be two graphs. Packing problem is to find in $G$ the largest number of independent subgraphs each of which is isomorphic to $H$. Let $U\subset{V}$. If the graph $G-U$ has no subgraph isomorphic to $H$, $U$ is a cover…

A 2-packing set for an undirected, weighted graph G=(V,E,w) is a subset S of the vertices V such that any two vertices are not adjacent and have no common neighbors. The Maximum Weight 2-Packing Set problem that asks for a 2-packing set of…

Given a graph, the sparsest cut problem asks for a subset of vertices whose edge expansion (the normalized cut given by the subset) is minimized. In this paper, we study a generalization of this problem seeking for $ k $ disjoint subsets of…

We consider the Densest-Subgraph problem, where a graph and an integer k is given and we search for a subgraph on exactly k vertices that induces the maximum number of edges. We prove that this problem is NP-hard even when the input graph…

We consider the classical $k$-Center problem in undirected graphs. The problem is known to have a polynomial-time 2-approximation. There are even $(2+\varepsilon)$-approximations running in near-linear time. The conventional wisdom is that…

For any fixed measure $H$ that maps graphs to real numbers, the MinH problem is defined as follows: given a graph $G$, an integer $k$, and a target $\tau$, is there a set $S$ of $k$ vertices that can be deleted, so that $H(G - S)$ is at…

A 2-packing set for an undirected graph $G=(V,E)$ is a subset $\mathcal{S} \subset V$ such that any two vertices $v_1,v_2 \in \mathcal{S}$ have no common neighbors. Finding a 2-packing set of maximum cardinality is a NP-hard problem. We…

Given a set $P$ of $n$ points in the plane and a collection of disks centered at these points, the disk graph $G(P)$ has vertex set $P$, with an edge between two vertices if their corresponding disks intersect. We study the dominating set…

Dense subgraph discovery is a fundamental problem in graph mining with a wide range of applications \cite{gionis2015dense}. Despite a large number of applications ranging from computational neuroscience to social network analysis, that take…

We consider several problems related to packing forests in graphs. The first one is to find $k$ edge-disjoint forests in a directed graph $G$ of maximal size such that the indegree of each vertex in these forests is at most $k$. We describe…

For a connected graph G=(V,E), a subset U of V is called a disconnected cut if U disconnects the graph and the subgraph induced by U is disconnected as well. We show that the problem to test whether a graph has a disconnected cut is…

A straightforward dynamic programming method for the single-source shortest paths problem (SSSP) in an edge-weighted directed acyclic graph (DAG) processes the vertices in a topologically sorted order. First, we similarly iterate this…

Given a graph $G$ and sets $\{\alpha_v~|~v \in V(G)\}$ and $\{\beta_v~|~v \in V(G)\}$ of non-negative integers, it is known that the decision problem whether $G$ contains a spanning tree $T$ such that $\alpha_v \le d_T (v) \le \beta_v $ for…

In the Disjoint Paths problem, the input consists of an $n$-vertex graph $G$ and a collection of $k$ vertex pairs, $\{(s_i,t_i)\}_{i=1}^k$, and the objective is to determine whether there exists a collection $\{P_i\}_{i=1}^k$ of $k$…

Many well-known NP-hard algorithmic problems on directed graphs resist efficient parametrisations with most known width measures for directed graphs, such as directed treewidth, DAG-width, Kelly-width and many others. While these focus on…

In the Vertex Disjoint Paths with Congestion problem, the input consists of a digraph $D$, an integer $c$ and $k$ pairs of vertices $(s_i, t_i)$, and the task is to find a set of paths connecting each $s_i$ to its corresponding $t_i$,…

We introduce a new graph-theoretic concept in the area of network monitoring. A set $M$ of vertices of a graph $G$ is a \emph{distance-edge-monitoring set} if for every edge $e$ of $G$, there is a vertex $x$ of $M$ and a vertex $y$ of $G$…

In this article, we revisit the complexity of the reconfiguration of independent sets under the token sliding rule on chordal graphs. In the \textsc{Token Sliding-Connectivity} problem, the input is a graph $G$ and an integer $k$, and the…