Related papers: An efficient algorithm to test forcibly-connectedn…

Let $G$ be a simple and finite graph without isolated vertices. In this paper we study forcing sets (zero forcing sets) which induce a subgraph of $G$ without isolated vertices. Such a set is called a total forcing set, introduced and first…

With the current burst of network theory (especially in connection with social and biological networks) there is a renewed interest on realizations of given degree sequences. In this paper we propose an essentially new degree sequence…

The notion of $P$-stability of an infinite set of degree sequences plays influential role in approximating the permanents, rapidly sampling the realizations of graphic degree sequences, or even studying and improving network privacy. While…

Generalizing the notion of split graphs to uniform hypergraphs, we prove that the class of these hypergraphs can be characterized by a finite list of excluded induced subhypergraphs. We show that a characterization by generalized degree…

Listing all triangles is a fundamental graph operation. Triangles can have important interpretations in real-world graphs, especially social and other interaction networks. Despite the lack of provably efficient (linear, or slightly…

A connected undirected graph $G=(V,E)$ is given. This paper presents an algorithm that samples (non-uniformly) a $K$ partition $U_1,\ldots U_K$ of the graph nodes $V$, such that the subgraph induced by each $U_k$, with $k=1:K$, is…

Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…

Motivated by recent computational models for redistricting and detection of gerrymandering, we study the following problem on graph partitions. Given a graph $G$ and an integer $k\geq 1$, a $k$-district map of $G$ is a partition of $V(G)$…

Problems of the following kind have been the focus of much recent research in the realm of parameterized complexity: Given an input graph (digraph) on $n$ vertices and a positive integer parameter $k$, find if there exist $k$ edges (arcs)…

We classify graphs that are 0, 1, or 2 edges short of being complete partite graphs with respect to intrinsic linking and intrinsic knotting. In addition, we classify intrinsic knotting of graphs on 8 vertices. For graphs in these families,…

An important family of span programs, st-connectivity span programs, have been used to design quantum algorithms in various contexts, including a number of graph problems and formula evaluation problems. The complexity of the resulting…

We study the problem of recognizing the cluster structure of a graph in the framework of property testing in the bounded degree model. Given a parameter $\varepsilon$, a $d$-bounded degree graph is defined to be $(k, \phi)$-clusterable, if…

Zero forcing is a dynamic graph coloring process whereby a colored vertex with a single uncolored neighbor forces that neighbor to be colored. This forcing process has been used to approximate certain linear algebraic parameters, as well as…

Given a small random sample of $n$-bit strings labeled by an unknown Boolean function, which properties of this function can be tested computationally efficiently? We show an equivalence between properties that are efficiently testable from…

For any simple graph $G$ on $n$ vertices, the (positive semi-definite) minimum rank of $G$ is defined to be the smallest possible rank among all (positive semi-definite) real symmetric $n\times n$ matrices whose entry in position $(i,j)$,…

Despite the exploding interest in graph neural networks there has been little effort to verify and improve their robustness. This is even more alarming given recent findings showing that they are extremely vulnerable to adversarial attacks…

We study a class of simple algorithms for concurrently computing the connected components of an $n$-vertex, $m$-edge graph. Our algorithms are easy to implement in either the COMBINING CRCW PRAM or the MPC computing model. For two related…

In the Split Vertex Deletion problem, given a graph G and an integer k, we ask whether one can delete k vertices from the graph G to obtain a split graph (i.e., a graph, whose vertex set can be partitioned into two sets: one inducing a…

In this paper we provide sub-linear algorithms for several fundamental problems in the setting in which the input graph excludes a fixed minor, i.e., is a minor-free graph. In particular, we provide the following algorithms for minor-free…

In this paper we propose an online approximate k-nn graph building algorithm, which is able to quickly update a k-nn graph using a flow of data points. One very important step of the algorithm consists in using the current distributed graph…