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Given a graph $G$ and a parameter $k$, the Chordal Vertex Deletion (CVD) problem asks whether there exists a subset $U\subseteq V(G)$ of size at most $k$ that hits all induced cycles of size at least 4. The existence of a polynomial kernel…
The Directed Feedback Vertex Set problem (DFVS) asks whether it is possible to remove at most $k$ vertices from a directed graph to make it acyclic. Whether DFVS is fixed-parameter tractable was a long-standing open problem in parameterized…
Many hard graph problems, such as Hamiltonian Cycle, become FPT when parameterized by treewidth, a parameter that is bounded only on sparse graphs. When parameterized by the more general parameter clique-width, Hamiltonian Cycle becomes…
We study the influence of a graph parameter called modular-width on the time complexity for optimally solving well-known polynomial problems such as Maximum Matching, Triangle Counting, and Maximum $s$-$t$ Vertex-Capacitated Flow. The…
We give an algorithm that takes as input an $n$-vertex graph $G$ and an integer $k$, runs in time $2^{O(k^2)} n^{O(1)}$, and outputs a tree decomposition of $G$ of width at most $k$, if such a decomposition exists. This resolves the…
Recently it was shown that many classic graph problems -- Independent Set, Dominating Set, Hamiltonian Cycle, and more -- can be solved in subexponential time on unit-ball graphs. More precisely, these problems can be solved in…
Many algorithms have been developed for NP-hard problems on graphs with small treewidth $k$. For example, all problems that are expressable in linear extended monadic second order can be solved in linear time on graphs of bounded treewidth.…
Linear rankwidth is a linearized variant of rankwidth, introduced by Oum and Seymour [Approximating clique-width and branch-width. J. Combin. Theory Ser. B, 96(4):514--528, 2006]. Motivated from recent development on graph modification…
A graph is $H$-free if it contains no induced subgraph isomorphic to $H$. We prove new complexity results for the two classical cycle transversal problems Feedback Vertex Set and Odd Cycle Transversal by showing that they can be solved in…
Dynamic programming on various graph decompositions is one of the most fundamental techniques used in parameterized complexity. Unfortunately, even if we consider concepts as simple as path or tree decompositions, such dynamic programming…
In the Partial Vertex Cover (PVC) problem, we are given an $n$-vertex graph $G$ and a positive integer $k$, and the objective is to find a vertex subset $S$ of size $k$ maximizing the number of edges with at least one end-point in $S$. This…
A locating-dominating set $D$ of a graph $G$ is a dominating set of $G$ where each vertex not in $D$ has a unique neighborhood in $D$, and the Locating-Dominating Set problem asks if $G$ contains such a dominating set of bounded size. This…
Given a graph $G$ and a positive integer $k$, the 2-Load coloring problem is to check whether there is a $2$-coloring $f:V(G) \rightarrow \{r,b\}$ of $G$ such that for every $i \in \{r,b\}$, there are at least $k$ edges with both end…
Given a planar graph $G$ and an integer $b$, OrthogonalPlanarity is the problem of deciding whether $G$ admits an orthogonal drawing with at most $b$ bends in total. We show that OrthogonalPlanarity can be solved in polynomial time if $G$…
In the Hedge Cut problem, the edges of a graph are partitioned into groups called hedges, and the question is what is the minimum number of hedges to delete to disconnect the graph. Ghaffari, Karger, and Panigrahi [SODA 2017] showed that…
The notion of $\mathcal{H}$-treewidth, where $\mathcal{H}$ is a hereditary graph class, was recently introduced as a generalization of the treewidth of an undirected graph. Roughly speaking, a graph of $\mathcal{H}$-treewidth at most $k$…
The graph homomorphism problem (HOM) asks whether the vertices of a given $n$-vertex graph $G$ can be mapped to the vertices of a given $h$-vertex graph $H$ such that each edge of $G$ is mapped to an edge of $H$. The problem generalizes the…
In this paper we consider Simultaneous Feedback Edge Set (Sim-FES) problem. In this problem, the input is an $n$-vertex graph $G$, an integer $k$ and a coloring function ${\sf col}: E(G) \rightarrow 2^{[\alpha]}$ and the objective is to…
We study the parameterized complexity of the Cograph Deletion problem, which asks whether one can delete at most $k$ edges from a graph to make it $P_4$-free. This is a well-known graph modification problem with applications in computation…
Let G be an input graph with n vertices and m edges and let k be a fixed parameter. We provide a single exponential FPT algorithm with running time O(c^kn(n+m)), c= min {18,k} that turns graph G into an interval graph by deleting at most k…