Related papers: A New Perspective on Vertex Connectivity
The core vertex set of a graph is an invariant of the graph. It consists of those vertices associated with the non-zero entries of the nullspace vectors of a $\{0,1\}$-adjacency matrix. The remaining vertices of the graph form the…
Given a set of nonempty subsets of some universal set, their intersection graph is defined as the graph with one vertex for each set and two vertices are adjacent precisely when their representing sets have non-empty intersection. Sometimes…
Answering connectivity queries is fundamental to fully dynamic graphs where edges and vertices are inserted and deleted frequently. Existing work proposes data structures and algorithms with worst-case guarantees. We propose a new data…
The online dominating set problem is an online variant of the minimum dominating set problem, which is one of the most important NP-hard problems on graphs. This problem is defined as follows: Given an undirected graph $G = (V, E)$, in…
Finding important edges in a graph is a crucial problem for various research fields, such as network epidemics, signal processing, machine learning, and sensor networks. In this paper, we tackle the problem based on sampling theory on…
We study the fine-grained complexity of graph connectivity problems in unweighted undirected graphs. Recent development shows that all variants of edge connectivity problems, including single-source-single-sink, global, Steiner,…
One of the most important questions in matroid optimization is to find disjoint common bases of two matroids. The significance of the problem is well-illustrated by the long list of conjectures that can be formulated as special cases.…
We study the problem of distance-preserving graph compression for weighted paths and trees. The problem entails a weighted graph $G = (V, E)$ with non-negative weights, and a subset of edges $E^{\prime} \subset E$ which needs to be removed…
The problem of finding the maximum number of vertex-disjoint uni-color paths in an edge-colored graph (called MaxCDP) has been recently introduced in literature, motivated by applications in social network analysis. In this paper we…
Compression and sparsification algorithms are frequently applied in a preprocessing step before analyzing or optimizing large networks/graphs. In this paper we propose and study a new framework contracting edges of a graph (merging vertices…
We introduce the concept of matching connectivity as a notion of connectivity in graph admitting perfect matchings which heavily relies on the structural properties of those matchings. We generalise a result of Robertson, Seymour and Thomas…
Driven by many applications in graph analytics, the problem of computing $k$-edge connected components ($k$-ECCs) of a graph $G$ for a user-given $k$ has been extensively studied recently. In this paper, we investigate the problem of…
We consider the problem of how much edge connectivity is necessary to force a graph G to contain a fixed graph H as an immersion. We show that if the maximum degree in H is D, then all the examples of D-edge connected graphs which do not…
Fair graph partition of social networks is a crucial step toward ensuring fair and non-discriminatory treatments in unsupervised user analysis. Current fair partition methods typically consider node balance, a notion pursuing a…
Given an undirected graph $G$ of $n$ weighted edges, stored one edge per processor in a square mesh of $n$ processors, we show how to determine the connected components and a minimal spanning forest in $\Theta(\sqrt{n})$ time. More…
Recently, a new way of avoiding crossings in straight-line drawings of non-planar graphs has been investigated. The idea of partial edge drawings (PED) is to drop the middle part of edges and rely on the remaining edge parts called stubs.…
The $c$-packedness property, proposed in 2010, is a geometric property that captures the spatial distribution of a set of edges. Despite the recent interest in $c$-packedness, its utility has so far been limited to Fr\'echet distance…
Consider a graph with nonnegative node weight. A vertex subset is called a CDS (connected dominating set) if every other node has at least one neighbor in the subset and the subset induces a connected subgraph. Furthermore, if every other…
An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V, E) and the goal is to find a subset of vertices S $\subseteq$ V that maximizes the number of edges in the cut \delta(S) such that the induced graph…
A dominating induced matching, also called an efficient edge domination, of a graph $G=(V,E)$ with $n=|V|$ vertices and $m=|E|$ edges is a subset $F \subseteq E$ of edges in the graph such that no two edges in $F$ share a common endpoint…