相关论文: Two-connected spanning subgraphs with at most $\fr…

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…

In the Activation Edge-Multicover problem we are given a multigraph $G=(V,E)$ with activation costs $\{c_{e}^u,c_{e}^v\}$ for every edge $e=uv \in E$, and degree requirements $r=\{r_v:v \in V\}$. The goal is to find an edge subset $J…

In the pairwise weighted spanner problem, the input consists of an $n$-vertex-directed graph, where each edge is assigned a cost and a length. Given $k$ vertex pairs and a distance constraint for each pair, the goal is to find a…

The problem of enumerating all connected induced subgraphs of a given order $k$ from a given graph arises in many practical applications: bioinformatics, information retrieval, processor design,to name a few. The upper bound on the number…

Increasing the connectivity of a graph is a pivotal challenge in robust network design. The weighted connectivity augmentation problem is a common version of the problem that takes link costs into consideration. The problem is then to find…

In this paper we consider the problem of computing the $2$-vertex-connected components ($2$-vccs) of directed graphs. We present two new algorithms for solving this problem. The first algorithm runs in $O(mn^{2})$ time, the second in…

In this paper we characterize the unique graph whose algebraic connectivity is minimum among all connected graphs with given order and fixed matching number or edge covering number, and present two lower bounds for the algebraic…

We investigate parameterized algorithms for the NP-hard problem Min-Power Asymmetric Connectivity (MinPAC) that has applications in wireless sensor networks. Given a directed arc-weighted graph, MinPAC asks for a strongly connected spanning…

The number of spanning trees in a graph $G$ is the total number of distinct spanning subgraphs of $G$ that are trees. In this paper we characterize the unique graph with a prescribed vertex (resp. edge) connectivity, minimum degree and…

We study the following Two-Sets Cut-Uncut problem on planar graphs. Therein, one is given an undirected planar graph $G$ and two sets of vertices $S$ and $T$. The question is, what is the minimum number of edges to remove from $G$, such…

A graph G is called (2k, k)-connected if G is 2k-edge-connected and G-v is k-edge-connected for every vertex v. The study of (2k, k)-connected graphs is motivated by a conjecture of Frank which states that a graph has a 2-vertex-connected…

Consider a setting where possibly sensitive information sent over a path in a network is visible to every {neighbor} of the path, i.e., every neighbor of some node on the path, thus including the nodes on the path itself. The exposure of a…

Let $G$ be a contraction critically quasi $5$-connected graph on at least $14$ vertices. If there is a vertex $x\in V_{4}(G)$ such that $G[N_{G}(x)]\cong K_{1,3}$ or $G[N_{G}(x)]\cong C_{4}$, then $G$ has a quasi $5$-contractible subgraph…

In the weighted minimum strongly connected spanning subgraph (WMSCSS) problem we must purchase a minimum-cost strongly connected spanning subgraph of a digraph. We show that half-integral linear program (LP) solutions for WMSCSS can be…

We present tight bounds on the spanning ratio of a large family of ordered $\theta$-graphs. A $\theta$-graph partitions the plane around each vertex into $m$ disjoint cones, each having aperture $\theta = 2 \pi/m$. An ordered $\theta$-graph…

The minimum-cost $k$-edge-connected spanning subgraph ($k$-ECSS) problem is a generalization and strengthening of the well-studied minimum-cost spanning tree (MST) problem. While the round complexity of distributedly computing the latter…

The MEG (minimum equivalent graph) problem is, given a directed graph, to find a small subset of the edges that maintains all reachability relations between nodes. The problem is NP-hard. This paper gives a proof that, for graphs where each…

How to draw the vertices of a complete multipartite graph $G$ on different points of a bounded $d$-dimensional integer grid, such that the sum of squared distances between vertices of $G$ is (i) minimized or (ii) maximized? For both…

Spanner constructions focus on the initial design of the network. However, networks tend to improve over time. In this paper, we focus on the improvement step. Given a graph and a budget $k$, which $k$ edges do we add to the graph to…

This paper deals with the problem of finding a collection of vertex-disjoint paths in a given graph G=(V,E) such that each path has at least four vertices and the total number of vertices in these paths is maximized. The problem is NP-hard…