Related papers: Fixed-parameter tractability of counting small min…
We study the directed global minimum vertex-cut problem: given a directed vertex-weighted graph $G$, compute a vertex-cut $(L,S,R)$ in $G$ of minimum value, which is defined to be the total weight of all vertices in $S$. The problem,…
Given a graph $G$ and an integer $k$, the Feedback Vertex Set (FVS) problem asks if there is a vertex set $T$ of size at most $k$ that hits all cycles in the graph. The fixed-parameter tractability status of FVS in directed graphs was a…
We propose a fixed-parameter tractable algorithm for the \textsc{Max-Cut} problem on embedded 1-planar graphs parameterized by the crossing number $k$ of the given embedding. A graph is called 1-planar if it can be drawn in the plane with…
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 propose two fixed-parameter tractable algorithms for the weighted Max-Cut problem on embedded 1-planar graphs parameterized by the crossing number $k$ of the given embedding. A graph is called 1-planar if it can be drawn in the plane…
In the Steiner Tree problem we are given an undirected edge-weighted graph as input, along with a set $K$ of vertices called terminals. The task is to output a minimum-weight connected subgraph that spans all the terminals. The famous…
We prove that finding a $k$-edge induced subgraph is fixed-parameter tractable, thereby answering an open problem of Leizhen Cai. Our algorithm is based on several combinatorial observations, Gauss' famous \emph{Eureka} theorem [Andrews,…
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…
We study multi-budgeted variants of the classic minimum cut problem and graph separation problems that turned out to be important in parameterized complexity: Skew Multicut and Directed Feedback Arc Set. In our generalization, we assign…
This paper revisits the classical Edge Disjoint Paths (EDP) problem, where one is given an undirected graph $G$ and a set of terminal pairs $P$ and asks whether $G$ contains a set of pairwise edge-disjoint paths connecting every terminal…
Let $G=(V,E)$ be a graph on $n$ vertices and $R$ be a set of pairs of vertices in $V$ called \emph{requests}. A \emph{multicut} is a subset $F$ of $E$ such that every request $xy$ of $R$ is cut by $F$, \i.e. every $xy$-path of $G$…
A stable cutset in a graph $G$ is a set $S\subseteq V(G)$ such that vertices of $S$ are pairwise non-adjacent and such that $G-S$ is disconnected, i.e., it is both stable (or independent) set and a cutset (or separator). Unlike general…
In the DELETION TO INDUCED MATCHING problem, we are given a graph $G$ on $n$ vertices, $m$ edges and a non-negative integer $k$ and asks whether there exists a set of vertices $S \subseteq V(G) $ such that $|S|\le k$ and the size of any…
We consider the (exact, minimum) $k$-cut problem: given a graph and an integer $k$, delete a minimum-weight set of edges so that the remaining graph has at least $k$ connected components. This problem is a natural generalization of the…
We provide a simple new randomized contraction approach to the global minimum cut problem for simple undirected graphs. The contractions exploit 2-out edge sampling from each vertex rather than the standard uniform edge sampling. We…
In the Topological Minor Deletion (TM-Deletion) problem input consists of an undirected graph $G$, a family of undirected graphs ${\cal F}$ and an integer $k$. The task is to determine whether $G$ contains a set of vertices $S$ of size at…
We consider the Shallow-Light Steiner Network problem from a fixed-parameter perspective. Given a graph $G$, a distance bound $L$, and $p$ pairs of vertices $(s_1,t_1),\cdots,(s_p,t_p)$, the objective is to find a minimum-cost subgraph $G'$…
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…
The Minimum Coloring Cut Problem is defined as follows: given a connected graph G with colored edges, find an edge cut E' of G (a minimal set of edges whose removal renders the graph disconnected) such that the number of colors used by the…
(see paper for full abstract) Cut problems and connectivity problems on digraphs are two well-studied classes of problems from the viewpoint of parameterized complexity. After a series of papers over the last decade, we now have (almost)…