Related papers: l-path vertex cover is easier than l-hitting set f…
The notion of Turing kernelization investigates whether a polynomial-time algorithm can solve an NP-hard problem, when it is aided by an oracle that can be queried for the answers to bounded-size subproblems. One of the main open problems…
A set cover of a hypergraph $H$ is a set of vertices intersecting every hyperedge. In the minimum sum set cover problem, vertices are selected one by one; each edge pays the position of the first vertex that hits it, and the objective is to…
We study the Minimum Sum Vertex Cover problem, which asks for an ordering of vertices in a graph that minimizes the total cover time of edges. In particular, n vertices of the graph are visited according to an ordering, and for each edge…
$H$-Packing is the problem of finding a maximum number of vertex-disjoint copies of $H$ in a given graph $G$. $H$-Partition is the special case of finding a set of vertex-disjoint copies that cover each vertex of $G$ exactly once. Our goal…
Covering problems belong to the foundation of graph theory. There are several types of covering problems in graph theory such as covering the vertex set by stars (domination problem), covering the vertex set by cliques (clique covering…
In the Feedback Vertex Set problem, one is given an undirected graph $G$ and an integer $k$, and one needs to determine whether there exists a set of $k$ vertices that intersects all cycles of $G$ (a so-called feedback vertex set). Feedback…
Given a clique-width $k$-expression of a graph $G$, we provide $2^{O(k)}\cdot n$ time algorithms for connectivity constraints on locally checkable properties such as Node-Weighted Steiner Tree, Connected Dominating Set, or Connected Vertex…
We study a generalization of the Set Cover problem called the \emph{Partial Set Cover} in the context of geometric set systems. The input to this problem is a set system $(X, \mathcal{S})$, where $X$ is a set of elements and $\mathcal{S}$…
The graph parameter vertex integrity measures how vulnerable a graph is to a removal of a small number of vertices. More precisely, a graph with small vertex integrity admits a small number of vertex removals to make the remaining connected…
Given a graph $G = (V,E)$, a set $T$ of vertex pairs, and an integer $k$, Hitting Geodesic Intervals asks whether there is a set $S \subseteq V$ of size at most $k$ such that for each terminal pair $\{u,v\} \in T$, the set $S$ intersects at…
Computing a (short) path between two vertices is one of the most fundamental primitives in graph algorithmics. In recent years, the study of paths in temporal graphs, that is, graphs where the vertex set is fixed but the edge set changes…
A $k$-matching cover of a graph $G$ is a union of $k$ matchings of $G$ which covers $V(G)$. A matching cover of $G$ is optimal if it consists of the fewest matchings of $G$. In this paper, we present an algorithm for finding an optimal…
We study the computational complexity of two well-known graph transversal problems, namely Subset Feedback Vertex Set and Subset Odd Cycle Transversal, by restricting the input to $H$-free graphs, that is, to graphs that do not contain some…
Deletion problems are those where given a graph $G$ and a graph property $\pi$, the goal is to find a subset of edges such that after its removal the graph $G$ will satisfy the property $\pi$. Typically, we want to minimize the number of…
Given an undirected graph $G=(V,E)$ with positive edge lengths and two vertices $s$ and $t$, the next-to-shortest path problem is to find an $st$-path which length is minimum amongst all $st$-paths strictly longer than the shortest path…
An edge dominating set of a graph G=(V,E) is a subset M of edges in the graph such that each edge in E-M is incident with at least one edge in M. In an instance of the parameterized edge dominating set problem we are given a graph G=(V,E)…
Minimum sum vertex cover of an $n$-vertex graph $G$ is a bijection $\phi : V(G) \to [n]$ that minimizes the cost $\sum_{\{u,v\} \in E(G)} \min \{\phi(u), \phi(v) \}$. Finding a minimum sum vertex cover of a graph (the MSVC problem) is…
Reachability and shortest path problems are NL-complete for general graphs. They are known to be in L for graphs of tree-width 2 [JT07]. However, for graphs of tree-width larger than 2, no bound better than NL is known. In this paper, we…
The Surjective Homomorphism problem is to test whether a given graph G called the guest graph allows a vertex-surjective homomorphism to some other given graph H called the host graph. The bijective and injective homomorphism problems can…
In this paper, we provide an algorithm for traversing geometric graphs which visits all vertices, and reports every vertex and edge exactly once. To achieve this, we combine a given geometric graph $G$ with the integer lattice, seen as a…