Related papers: Central limit theorems for combinatorial optimizat…
We consider the edge-triangle model, a two-parameter family of exponential random graphs in which dependence between edges is introduced through triangles. In the so-called replica symmetric regime, the limiting free energy exists together…
In the random geometric graph $G(n,r_n)$, $n$ vertices are placed randomly in Euclidean $d$-space and edges are added between any pair of vertices distant at most $r_n$ from each other. We establish strong laws of large numbers (LLNs) for a…
In this paper we introduce a general framework for proving lower bounds for various Ramsey type problems within random settings. The main idea is to view the problem from an algorithmic perspective: we aim at providing an algorithm that…
In this paper we introduce a general framework for the study of limits of relational structures in general and graphs in particular, which is based on a combination of model theory and (functional) analysis. We show how the various…
We introduce a method for the theoretical analysis of exponential random graph models. The method is based on a large-deviations approximation to the normalizing constant shown to be consistent using theory developed by Chatterjee and…
We use the recently developed method of weighted dependency graphs to prove central limit theorems for the number of occurrences of any fixed pattern in multiset permutations and in set partitions. This generalizes results for patterns of…
A dominating set $D$ of a graph $G$ is a set of vertices such that any vertex in $G$ is in $D$ or its neighbor is in $D$. Enumeration of minimal dominating sets in a graph is one of central problems in enumeration study since enumeration of…
The linear complementarity problem is a continuous optimization problem that generalizes convex quadratic programming, Nash equilibria of bimatrix games and several such problems. This paper presents a continuous optimization formulation…
A central limit theorem for arrays of symmetric row-wise exchangeable random variables is presented. The result is valid for finite and infinite extendable and non-extendable sequences. Unlike most reported versions of the central limit…
The maximum independent set problem is one of the most important problems in graph algorithms and has been extensively studied in the line of research on the worst-case analysis of exact algorithms for NP-hard problems. In the weighted…
We address the issue of the Central Limit Theorem for (both local and global) empirical measures of diffusions interacting on a possibly diluted Erd\H{o}s-R\'enyi graph. Special attention is given to the influence of initial condition (not…
In this paper we consider a dynamic version of the Erd\H{o}s-R\'{e}nyi random graph, in which edges independently appear and disappear in time, with the on- and off times being exponentially distributed. The focus lies on the evolution of…
Problems from metric graph theory like Metric Dimension, Geodetic Set, and Strong Metric Dimension have recently had a strong impact in parameterized complexity by being the first known problems in NP to admit double-exponential lower…
We study correlation decay for the maximum weight matching problem on sparse graphs with i.i.d. edge weights. We show exponential decay of correlations when the underlying graphs are locally tree-like with uniformly bounded degree and the…
Many important theorems in combinatorics, such as Szemer\'edi's theorem on arithmetic progressions and the Erd\H{o}s-Stone Theorem in extremal graph theory, can be phrased as statements about independent sets in uniform hypergraphs. In…
We present a rather general method for proving local limit theorems, with a good rate of convergence, for sums of dependent random variables. The method is applicable when a Stein coupling can be exhibited. Our approach involves both…
We study the problem of robustly estimating the edge density of Erd\H{o}s-R\'enyi random graphs $G(n, d^\circ/n)$ when an adversary can arbitrarily add or remove edges incident to an $\eta$-fraction of the nodes. We develop the first…
We study inhomogeneous random graphs with a finite type space. For a natural generalization of the model as a dynamic network-valued process, the paper establishes the following results: (a) Functional central limit theorems for the…
We study a well known noisy model of the graph isomorphism problem. In this model, the goal is to perfectly recover the vertex correspondence between two edge-correlated Erd\H{o}s-R\'{e}nyi random graphs, with an initial seed set of…
The main result of the paper is motivated by the following two, apparently unrelated graph optimization problems: (A) as an extension of Edmonds' disjoint branchings theorem, characterize digraphs comprising $k$ disjoint branchings $B_i$…