Related papers: Making Bidirected Graphs Strongly Connected
We study the minimum cut problem in the presence of uncertainty and show how to apply a novel robust optimization approach, which aims to exploit the similarity in subsequent graph measurements or similar graph instances, without posing any…
Bach et al. [1] recently presented an algorithm for constructing confluent drawings, by leveraging power graph decomposition to generate an auxiliary routing graph. We identify two issues with their method which we call the node split and…
We show that if a graph is k-edge-connected, and we adjoin to it another graph satisfying a "contracted diameter less or equal to 2" condition, with minimal degree greater or equal to k, and some natural hypothesis on the edges connecting…
The shortest path problem in graphs is a cornerstone of AI theory and applications. Existing algorithms generally ignore edge weight computation time. We present a generalized framework for weighted directed graphs, where edge weight can be…
A bipartite graph $G=(U,V,E)$ is convex if the vertices in $V$ can be linearly ordered such that for each vertex $u\in U$, the neighbors of $u$ are consecutive in the ordering of $V$. An induced matching $H$ of $G$ is a matching such that…
In this paper we consider two natural notions of connectivity for hypergraphs: weak and strong. We prove that the strong vertex connectivity of a connected hypergraph is bounded by its weak edge connectivity, thereby extending a theorem of…
Designing well-connected graphs is a fundamental problem that frequently arises in various contexts across science and engineering. The weighted number of spanning trees, as a connectivity measure, emerges in numerous problems and plays a…
Reconfiguring two shortest paths in a graph means modifying one shortest path to the other by changing one vertex at a time so that all the intermediate paths are also shortest paths. This problem has several natural applications, namely:…
A graph is temporally connected if there exists a strict temporal path, i.e. a path whose edges have strictly increasing labels, from every vertex $u$ to every other vertex $v$. In this paper we study temporal design problems for undirected…
Many problems in computational geometry are not stated in graph-theoretic terms, but can be solved efficiently by constructing an auxiliary graph and performing a graph-theoretic algorithm on it. Often, the efficiency of the algorithm…
In the matching interdiction problem, we are given an undirected graph with weights and interdiction costs on the edges and seek to remove a subset of the edges constrained to some budget, such that the weight of a maximum weight matching…
For bipartite graphs the NP-completeness is proved for the problem of existence of maximum matching which removal leads to a graph with given lower(upper)bound for the cardinality of its maximum matching.
In the Matching Cut problem we ask whether a graph $G$ has a matching cut, that is, a matching which is also an edge cut of $G$. We consider the variants Perfect Matching Cut and Disconnected Perfect Matching where we ask whether there…
One must add arrows which are forced by transitivity to form the transitive closure of a directed graph. We introduce a construction of a transitive directed graph which is formed by adding vertices instead of arrows and which preserves the…
In this paper, we present an on-line fully dynamic algorithm for maintaining strongly connected component of a directed graph in a shared memory architecture. The edges and vertices are added or deleted concurrently by fixed number of…
Finding a d-regular spanning subgraph (or d-factor) of a graph is easy by Tutte's reduction to the matching problem. By the same reduction, it is easy to find a minimal or maximal d-factor of a graph. However, if we require that the…
Here the All-pairs shortest path problem on weighted undirected sparse graphs is being considered. For the problem considered, we propose ``disassembly and assembly of a graph'' algorithm which uses a solution of the problem on a…
The analysis of networks characterized by links with heterogeneous intensity or weight suffers from two long-standing problems of arbitrariness. On one hand, the definitions of topological properties introduced for binary graphs can be…
We give an upper bound on the number of perfect matchings in simple graphs with a given number of vertices and edges. We apply this result to give an upper bound on the number of 2-factors in a directed complete bipartite balanced graph on…
In graph theory, the longest path problem is the problem of finding a simple path of maximum length in a given graph. For some small classes of graphs, the problem can be solved in polynomial time [2, 4], but it remains NP-hard on general…