Related papers: Revisiting a Successful Reduction Rule for Dominat…

Motivated by applications in network epidemiology, we consider the problem of determining whether it is possible to delete at most $k$ edges from a given input graph (of small treewidth) so that the resulting graph avoids a set…

We consider the fundamental problems of determining the rooted and global edge and vertex connectivities (and computing the corresponding cuts) in directed graphs. For rooted (and hence also global) edge connectivity with small integer…

We present a randomized algorithm for dynamic graph connectivity. With failure probability less than $1/n^c$ (for any constant $c$ we choose), our solution has worst case running time $O(\log^3 n)$ per edge insertion, $O(\log^4 n)$ per edge…

We study the dominating set problem in an online setting. An algorithm is required to guarantee competitiveness against an adversary that reveals the input graph one node at a time. When a node is revealed, the algorithm learns about the…

The {Congested Clique} is a distributed-computing model for single-hop networks with restricted bandwidth that has been very intensively studied recently. It models a network by an $n$-vertex graph in which any pair of vertices can…

The study of power domination in graphs arises from the problem of placing a minimum number of measurement devices in an electrical network while monitoring the entire network. A power dominating set of a graph is a set of vertices from…

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…

We introduce a new dynamic data structure for maintaining the strongly connected components (SCCs) of a directed graph (digraph) under edge deletions, so as to answer a rich repertoire of connectivity queries. Our main technical…

We present an algorithm to compute the domination polynomial of the $m \times n$ grid, cylinder, and torus graphs and the king graph. The time complexity of the algorithm is $O(m^2n^2 \lambda^{2m})$ for the torus and $O(m^3n^2\lambda^m)$…

A mixed dominating set for a graph $G = (V,E)$ is a set $S\subseteq V \cup E$ such that every element $x \in (V \cup E) \backslash S$ is either adjacent or incident to an element of $S$. The mixed domination number of a graph $G$, denoted…

We present a deterministic algorithm which, given a graph G with n vertices and an integer 1<m < n, computes in n^{O(ln m)} time the sum of weights w(S) over all m-subsets S of the set of vertices of G, where w(S)=exp{gamma t m +O(1/m)}…

A set $D\subseteq V$ of a graph $G=(V,E)$ is called a restrained dominating set of $G$ if every vertex not in $D$ is adjacent to a vertex in $D$ and to a vertex in $V \setminus D$. The \textsc{Minimum Restrained Domination} problem is to…

We introduce a novel multivariate approach for solving weighted parameterized problems. In our model, given an instance of size $n$ of a minimization (maximization) problem, and a parameter $W \geq 1$, we seek a solution of weight at most…

Considering a communication topology of a wireless network modeled by a graph where an edge exists between two nodes if they are within each other's communication range. A subset $U$ of nodes is a dominating set if each node is either in…

In this paper, we study the problem of deciding whether the total domination number of a given graph $G$ can be reduced using exactly one edge contraction (called 1-Edge Contraction($\gamma_t$)). We focus on several graph classes and…

Given a graph $G$ with $n$ vertices and maximum degree $\Delta$, it is known that $G$ admits a vertex coloring with $\Delta + 1$ colors such that no edge of $G$ is monochromatic. This can be seen constructively by a simple greedy algorithm,…

We revisit the algorithmic problem of finding a triangle in a graph: We give a randomized combinatorial algorithm for triangle detection in a given $n$-vertex graph with $m$ edges running in $O(n^{7/3})$ time, or alternatively in…

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…

This papers focuses on the average order of dominating sets of a graph. We find the extremal graphs for the maximum and minimum value over all graphs on $n$ vertices, while for trees we prove that the star minimizes the average order of…

We present two algorithms for maintaining the topological order of a directed acyclic graph with n vertices, under an online edge insertion sequence of m edges. Efficient algorithms for online topological ordering have many applications,…