Related papers: A Simple Test on 2-Vertex- and 2-Edge-Connectivity
We present a certifying algorithm that tests graphs for 3-edge-connectivity; the algorithm works in linear time. If the input graph is not 3-edge-connected, the algorithm returns a 2-edge-cut. If it is 3-edge-connected, it returns a…
Two planar graphs G1 and G2 sharing some vertices and edges are `simultaneously planar' if they have planar drawings such that a shared vertex [edge] is represented by the same point [curve] in both drawings. It is an open problem whether…
A linear-time certifying algorithm for 3-edge-connectivity is presented. Given an undirected graph G, if G is 3-edge-connected, the algorithm generates a construction sequence as a positive certificate for G. Otherwise, the algorithm…
Vertex connectivity and edge connectivity are fundamental concepts in graph theory that have been widely studied from both structural and algorithmic perspectives. The focus of this paper is on computing these two parameters for graphs…
Edge and vertex connectivity are fundamental concepts in graph theory. While they have been thoroughly studied in the case of undirected graphs, surprisingly not much has been investigated for directed graphs. In this paper we study…
A linear-time algorithm for generating auxiliary subgraphs for the 3-edge-connected components of a connected multigraph is presented. The algorithm uses an innovative graph contraction operation and makes only one pass over the graph. By…
Bipartite graphs model the relationships between two disjoint sets of entities in several applications and are naturally drawn as 2-layer graph drawings. In such drawings, the two sets of entities (vertices) are placed on two parallel lines…
In this work, for the given adjacency matrix of a graph, we present an algorithm which checks the connectivity of a graph and computes all of its connected components. Also, it is mathematically proved that the algorithm presents all the…
We provide algorithms for the minimum 2-edge-connected spanning subgraph problem and the minimum 2-vertex-connected spanning subgraph problem with approximation ratio both $\frac{4}{3}$. Using a common theme, the algorithms and their…
We complement our study of 2-connectivity in directed graphs, by considering the computation of the following 2-vertex-connectivity relations: We say that two vertices v and w are 2-vertex-connected if there are two internally…
The intersection graph of a collection of trapezoids with corner points lying on two parallel lines is called a trapezoid graph. These graphs and their generalizations were applied in various fields, including modeling channel routing…
We present faster algorithms for computing the 2-edge and 2-vertex strongly connected components of a directed graph, which are straightforward generalizations of strongly connected components. While in undirected graphs the 2-edge and…
On an evolving graph that is continuously updated by a high-velocity stream of edges, how can one efficiently maintain if two vertices are connected? This is the connectivity problem, a fundamental and widely studied problem on graphs. We…
We present a simple iterative strategy for measuring the connection strength between a pair of vertices in a graph. The method is attractive in that it has a linear complexity and can be easily parallelized. Based on an analysis of the…
We present the first linear-time algorithm that computes the $4$-edge-connected components of an undirected graph. Hence, we also obtain the first linear-time algorithm for testing $4$-edge connectivity. Our results are based on a…
Graph connectivity is a fundamental combinatorial optimization problem that arises in many practical applications, where usually a spanning subgraph of a network is used for its operation. However, in the real world, links may fail…
Connectivity query processing is a fundamental problem in graph processing. Given an undirected graph and two query vertices, the problem aims to identify whether they are connected via a path. Given frequent edge updates in real graph…
A graph is componentwise biconnected if every connected component either is an isolated vertex or is biconnected. We present a linear-time algorithm for the problem of adding the smallest number of edges to make a bipartite graph…
Consider the following problem: given a graph with edge costs and a subset Q of vertices, find a minimum-cost subgraph in which there are two edge-disjoint paths connecting every pair of vertices in Q. The problem is a failure-resilient…
Given a connected undirected multigraph G (a graph that may contain parallel edges), the algorithm of [19] finds the 3-edge-connected components of $G$ in linear time using an innovative graph contraction technique based on a depth-first…