Related papers: An ETH-Tight FPT Algorithm for Rejection-Proof Set…
An \emph{$H$-packing} in a graph $G$ is a collection of pairwise vertex-disjoint copies of $H$ in $G$. We prove that for every $c > 0$ and every bipartite graph $H$, any $\lfloor cn \rfloor$-regular graph $G$ admits an $H$-packing that…
Given a graph $G=(V,E)$, the dominating set problem asks for a minimum subset of vertices $D\subseteq V$ such that every vertex $u\in V\setminus D$ is adjacent to at least one vertex $v\in D$. That is, the set $D$ satisfies the condition…
In the Maximum Independent Set problem we are asked to find a set of pairwise nonadjacent vertices in a given graph with the maximum possible cardinality. In general graphs, this classical problem is known to be NP-hard and hard to…
We study the problem of efficiently refuting the k-colorability of a graph, or equivalently certifying a lower bound on its chromatic number. We give formal evidence of average-case computational hardness for this problem in sparse random…
A variant of the well-known Set Covering Problem is studied in this paper, where subsets of a collection have to be selected, and pairwise conflicts among subsets of items exist. The selection of each subset has a cost, and the inclusion of…
Given a graph, the general problem to cover the maximum number of vertices by a collection of vertex-disjoint long paths seemingly escapes from the literature. A path containing at least $k$ vertices is considered long. When $k \le 3$, the…
Vertex deletion and edge deletion problems play a central role in Parameterized Complexity. Examples include classical problems like Feedback Vertex Set, Odd Cycle Transversal, and Chordal Deletion. Interestingly, the study of edge…
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 present a new greedy rounding algorithm for the Cycle Packing Problem for uncrossable cycle families in planar graphs. This improves the best-known upper bound for the integrality gap of the natural packing LP to a constant slightly less…
A vertex set $D$ in a finite undirected graph $G$ is an {\em efficient dominating set} (\emph{e.d.s.}\ for short) of $G$ if every vertex of $G$ is dominated by exactly one vertex of $D$. The \emph{Efficient Domination} (ED) problem, which…
We study edge-labelings of the complete bidirected graph $\overset{\tiny\leftrightarrow}{K}_n$ with functions from the set $[d] = \{1, \dots, d\}$ to itself. We call a cycle in $\overset{\tiny\leftrightarrow}{K}_n$ a fixed-point cycle if…
The $H$-Free Edge Deletion problem asks, for a given graph $G$ and an integer $k$, whether it is possible to delete at most $k$ edges from $G$ to make it $H$-free, that is, not containing $H$ as an induced subgraph. The $H$-Free Edge…
The problem of modifying a given graph to satisfy certain properties has been one of the central topics in parameterized tractability study. In this paper, we study the cycle contraction problem, which makes a graph into a cycle by edge…
The Set Packing problem is, given a collection of sets $\mathcal{S}$ over a ground set $\mathcal{U}$, to find a maximum collection of sets that are pairwise disjoint. The problem is among the most fundamental NP-hard optimization problems…
In the Independent set problem, the input is a graph $G$, every vertex has a non-negative integer weight, and the task is to find a set $S$ of pairwise non-adjacent vertices, maximizing the total weight of the vertices in $S$. We give an…
Given a set of points $P$ and axis-aligned rectangles $\mathcal{R}$ in the plane, a point $p \in P$ is called \emph{exposed} if it lies outside all rectangles in $\mathcal{R}$. In the \emph{max-exposure problem}, given an integer parameter…
The Cut & Count technique and the rank-based approach have lead to single-exponential FPT algorithms parameterized by treewidth, that is, running in time $2^{O(tw)}n^{O(1)}$, for Feedback Vertex Set and connected versions of the classical…
The paper presents an algorithm for minimum vertex cover problem, which is an NP-Complete problem. The algorithm computes a minimum vertex cover of each input simple graph. Tested by the attached MATLAB programs, Stage 1 of the algorithm is…
We study the problem of fairly allocating a set of indivisible goods among $n$ agents with additive valuations. Envy-freeness up to any good (EFX) is arguably the most compelling fairness notion in this context. However, the existence of…
We consider the parameterized complexity of the problem of tracking shortest s-t paths in graphs, motivated by applications in security and wireless networks. Given an undirected and unweighted graph with a source s and a destination t,…