Related papers: Multi-cyclic graphs in the random graph process wi…

Inspired by artistic practices such as beadwork and himmeli, we study the problem of threading a single string through a set of tubes, so that pulling the string forms a desired graph. More precisely, given a connected graph (where edges…

We study the random planar graph process introduced by Gerke, Schlatter, Steger, and Taraz [The random planar graph process, Random Structures Algorithms 32 (2008), no. 2, 236--261; MR2387559]: Begin with an empty graph on $n$ vertices,…

We consider the problem of estimating undirected triangle-free graphs of high dimensional distributions. Triangle-free graphs form a rich graph family which allows arbitrary loopy structures but 3-cliques. For inferential tractability, we…

In the standard CONGEST model for distributed network computing, it is known that "global" tasks such as minimum spanning tree, diameter, and all-pairs shortest paths, consume large bandwidth, for their running-time is…

We consider the problem of finding all allowed edges in a bipartite graph $G=(V,E)$, i.e., all edges that are included in some maximum matching. We show that given any maximum matching in the graph, it is possible to perform this…

This paper presents a novel theoretical Monte Carlo Markov chain procedure in the framework of graphs. It specifically deals with the construction of a Markov chain whose empirical distribution converges to a given reference one. The Markov…

The MaxCut problem asks for the size ${\rm mc}(G)$ of a largest cut in a graph $G$. It is well known that ${\rm mc}(G)\ge m/2$ for any $m$-edge graph $G$, and the difference ${\rm mc}(G)-m/2$ is called the surplus of $G$. The study of the…

We study the problem of constructing cycle bases of graphs with low maximum edge participation, defined as the maximum number of basis cycles that share any single edge. This quantity, though less studied than total weight or length, plays…

The problem of graphical model selection is to correctly estimate the graph structure of a Markov random field given samples from the underlying distribution. We analyze the information-theoretic limitations of the problem of graph…

A separating system of a graph $G$ is a family $\mathcal{S}$ of subgraphs of $G$ for which the following holds: for all distinct edges $e$ and $f$ of $G$, there exists an element in $\mathcal{S}$ that contains $e$ but not $f$. Recently, it…

M\"omke and Svensson presented a beautiful new approach for the traveling salesman problem on a graph metric (graph-TSP), which yields a $4/3$-approximation guarantee on subcubic graphs as well as a substantial improvement over the…

We consider the problem of incremental cycle detection and topological ordering in a directed graph $G = (V, E)$ with $|V| = n$ nodes. In this setting, initially the edge-set $E$ of the graph is empty. Subsequently, at each time-step an…

Let $G$ be a graph with $m$ edges and let $\mathrm{mc}(G)$ denote the size of a largest cut of $G$. The difference $\mathrm{mc}(G)-m/2$ is called the surplus $\mathrm{sp}(G)$ of $G$. A fundamental problem in MaxCut is to determine…

We develop a sparse graph regularity method that applies to graphs with few 4-cycles, including new counting and removal lemmas for 5-cycles in such graphs. Some applications include: * Every $n$-vertex graph with no 5-cycle can be made…

We revisit the problem of counting the number of copies of a fixed graph in a random graph or multigraph, including the case of constrained degrees. Our approach relies heavily on analytic combinatorics and on the notion of patchwork to…

The generalised random graph contains $n$ vertices with positive i.i.d. weights. The probability of adding an edge between two vertices is increasing in their weights. We require the weight distribution to have finite second moments and…

The semi-random graph process is a single player game in which the player is initially presented an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the player independently and uniformly at random. The player then…

This paper aims to maximize algebraic connectivity of networks via topology design under the presence of constraints and an adversary. We are concerned with three problems. First, we formulate the concave maximization topology design…

We study a new algorithmic process of graph growth which starts from a single initial vertex and operates in discrete time-steps, called \emph{slots}. In every slot, the graph grows via two operations (i) vertex generation and (ii) edge…

We study experiment design for unique identification of the causal graph of a simple SCM, where the graph may contain cycles. The presence of cycles in the structure introduces major challenges for experiment design as, unlike acyclic…