Related papers: Parameterizing edge modification problems above lo…

In Path Set Packing, the input is an undirected graph $G$, a collection $\calp$ of simple paths in $G$, and a positive integer $k$. The problem is to decide whether there exist $k$ edge-disjoint paths in $\calp$. We study the parameterized…

For a set of graphs $\mathcal{H}$, the \textsc{$\mathcal{H}$-free Edge Deletion} problem asks to find whether there exist at most $k$ edges in the input graph whose deletion results in a graph without any induced copy of $H\in\mathcal{H}$.…

We study the parameterized complexity of separating a small set of vertices from a graph by a small vertex-separator. That is, given a graph $G$ and integers $k$, $t$, the task is to find a vertex set $X$ with $|X| \le k$ and $|N(X)| \le…

For graphs $G$ and $H$, an $H$-coloring of $G$ is an edge-preserving mapping from $V(G)$ to $V(H)$. In the $H$-Coloring problem the graph $H$ is fixed and we ask whether an instance graph $G$ admits an $H$-coloring. A generalization of this…

For a family of graphs $\mathcal{G}$, the $\mathcal{G}$-\textsc{Contraction} problem takes as an input a graph $G$ and an integer $k$, and the goal is to decide if there exists $F \subseteq E(G)$ of size at most $k$ such that $G/F$ belongs…

Let ${\cal G}$ be a minor-closed graph class and let $G$ be an $n$-vertex graph. We say that $G$ is a $k$-apex of ${\cal G}$ if $G$ contains a set $S$ of at most $k$ vertices such that $G\setminus S$ belongs to ${\cal G}$. Our first result…

We determine, up to a multiplicative constant, the optimal number of random edges that need to be added to a $k$-graph $H$ with minimum vertex degree $\Omega(n^{k-1})$ to ensure an $F$-factor with high probability, for any $F$ that belongs…

Let $H=(V(H),E(H))$ be a graph. A $k$-coloring of $H$ is a mapping $\pi : V(H) \longrightarrow \{1,2,\ldots, k\}$ so that each color class induces a $K_2$-free subgraph. For a graph $G$ of order at least $2$, a $G$-free $k$-coloring of $H$…

We study how to sparsify connectivity in graphs under a tight deletion budget. Given a graph $G$ and integers $k,x \ge 0$, Critical Node Cut (CNC) asks whether we can delete at most $k$ vertices so that the number of remaining unordered…

Given a graph $G$ and an integer $k$, the $H$-free Edge Deletion problem asks whether there exists a set of at most $k$ edges of $G$ whose deletion makes $G$ free of induced copies of $H$. Significant attention has been given to the…

In this paper we design {\sf FPT}-algorithms for two parameterized problems. The first is \textsc{List Digraph Homomorphism}: given two digraphs $G$ and $H$ and a list of allowed vertices of $H$ for every vertex of $G$, the question is…

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…

We study the \textsc{Labeled Contractibility} problem, where the input consists of two vertex-labeled graphs $G$ and $H$, and the goal is to determine whether $H$ can be obtained from $G$ via a sequence of edge contractions. Lafond and…

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,…

Given a graph $G = (V,E)$, a threshold function $t~ :~ V \rightarrow \mathbb{N}$ and an integer $k$, we study the Harmless Set problem, where the goal is to find a subset of vertices $S \subseteq V$ of size at least $k$ such that every…

For a fixed set ${\cal H}$ of graphs, a graph $G$ is ${\cal H}$-subgraph-free if $G$ does not contain any $H \in {\cal H}$ as a (not necessarily induced) subgraph. A recently proposed framework gives a complete classification on ${\cal…

Given a graph class $\mathcal{H}$, the task of the $\mathcal{H}$-Square Root problem is to decide, whether an input graph $G$ has a square root $H$ from $\mathcal{H}$. We are interested in the parameterized complexity of the problem for…

We consider a the minimum k-way cut problem for unweighted graphs with a size bound s on the number of cut edges allowed. Thus we seek to remove as few edges as possible so as to split a graph into k components, or report that this requires…

In the $\ell$-Coloring Problem, we are given a graph on $n$ nodes, and tasked with determining if its vertices can be properly colored using $\ell$ colors. In this paper we study below-guarantee graph coloring, which tests whether an…

Let F be a finite set of graphs. In the F-Deletion problem, we are given an n-vertex graph G and an integer k as input, and asked whether at most k vertices can be deleted from G such that the resulting graph does not contain a graph from F…