Related papers: A Refined Kernel for $d$-Hitting Set
We study the complexity of a generic hitting problem H-Subgraph Hitting, where given a fixed pattern graph $H$ and an input graph $G$, the task is to find a set $X \subseteq V(G)$ of minimum size that hits all subgraphs of $G$ isomorphic to…
We consider the algorithmic decision problem that takes as input an $n$-vertex $k$-uniform hypergraph $H$ with minimum codegree at least $m-c$ and decides whether it has a matching of size $m$. We show that this decision problem is fixed…
For a fixed simple digraph $H$ without isolated vertices, we consider the problem of deleting arcs from a given tournament to get a digraph which does not contain $H$ as an immersion. We prove that for every $H$, this problem admits a…
K-core decomposition is a commonly used metric to analyze graph structure or study the relative importance of nodes in complex graphs. Recent years have seen rapid growth in the scale of the graph, especially in industrial settings. For…
For a hypergraph $\mathcal{H}$, define the minimum positive codegree $\delta_i^+(\mathcal{H})$ to be the largest integer $k$ such that every $i$-set which is contained in at least one edge of $\mathcal{H}$ is contained in at least $k$…
We study kernelization of classic hard graph problems when the input graphs fulfill triadic closure properties. More precisely, we consider the recently introduced parameters closure number $c$ and the weak closure number $\gamma$ [Fox et…
Dominating set problems are among the most important class of combinatorial problems in graph optimization, from a theoretical as well as from a practical point of view. In this paper, we address the recently introduced (minimum) weighted…
We give an algorithmic and lower-bound framework that facilitates the construction of subexponential algorithms and matching conditional complexity bounds. It can be applied to intersection graphs of similarly-sized fat objects, yielding…
It has been shown that the maximum stable set problem in some infinite graphs, and the kissing number problem in particular, reduces to a minimization problem over the cone of copositive kernels. Optimizing over this infinite dimensional…
In this paper, we investigate three fundamental problems regarding cut complexes of graphs: their realizability, the uniqueness of graph reconstruction from them, and their algorithmic recognition. We define the parameter $m(d,n)$ as the…
The field of kernelization studies polynomial-time preprocessing routines for hard problems in the framework of parameterized complexity. Although a framework for proving kernelization lower bounds has been discovered in 2008 and…
The Connected Vertex Cover problem, where the goal is to compute a minimum set of vertices in a given graph which forms a vertex cover and induces a connected subgraph, is a fundamental combinatorial problem and has received extensive…
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…
Let $\mathcal{Q}$ be a vertex subset problem on graphs. In a reconfiguration variant of $\mathcal{Q}$ we are given a graph $G$ and two feasible solutions $S_s, S_t\subseteq V(G)$ of $\mathcal{Q}$ with $|S_s|=|S_t|=k$. The problem is to…
We study the complexity of the Hitting Set problem in set systems (hypergraphs) that avoid certain sub-structures. In particular, we characterize the classical and parameterized complexity of the problem when the Vapnik-Chervonenkis…
For a fixed graph $H$, the $H$-free-editing problem asks whether we can modify a given graph $G$ by adding or deleting at most $k$ edges such that the resulting graph does not contain $H$ as an induced subgraph. The problem is known to be…
A tournament T=(V,A) is a directed graph in which there is exactly one arc between every pair of distinct vertices. Given a digraph on n vertices and an integer parameter k, the Feedback Arc Set problem asks whether the given digraph has a…
In this paper, we consider the following two problems: (i) Deletion Blocker($\alpha$) where we are given an undirected graph $G=(V,E)$ and two integers $k,d\geq 1$ and ask whether there exists a subset of vertices $S\subseteq V$ with…
Let $d$ and $n$ be integers satisfying $C\leq d\leq \exp(c\sqrt{\ln n})$ for some universal constants $c, C>0$, and let $z\in \mathbb{C}$. Denote by $M$ the adjacency matrix of a random $d$-regular directed graph on $n$ vertices. In this…
Consider a random hypergraph on a set of N vertices in which, for k between 1 and N, a Poisson(N beta_k) number of hyperedges is scattered randomly over all subsets of size k. We collapse the hypergraph by running the following algorithm to…