Related papers: RSB bounds on the maximum cut
The fault tolerance of random graphs with unbounded degrees with respect to connectivity is investigated, which relates to the reliability of wireless sensor networks with unreliable relay nodes. The model evaluates the network breakdown…
We give lower bounds on the maximum possible girth of an $r$-uniform, $d$-regular hypergraph with at most $n$ vertices, using the definition of a hypergraph cycle due to Berge. These differ from the trivial upper bound by an absolute…
Ricci curvature was proposed by Ollivier in a general framework of metric measure spaces, and it has been studied extensively in the context of graphs in recent years. In this paper we prove upper bounds for Ollivier's Ricci curvature for…
Estimating numerically the spectral radius of a random walk on a nonamenable graph is complicated, since the cardinality of balls grows exponentially fast with the radius. We propose an algorithm to get a bound from below for this spectral…
We consider the problem of estimating the graph size, where one is given only local access to the graph. We formally define a query model in which one starts with a \emph{seed} node and is allowed to make queries about neighbours of nodes…
We consider the problem of finding lower bounds on the I/O complexity of arbitrary computations in a two level memory hierarchy. Executions of complex computations can be formalized as an evaluation order over the underlying computation…
Twin-width is a recently introduced graph parameter based on the repeated contraction of near-twins. It has shown remarkable utility in algorithmic and structural graph theory, as well as in finite model theory -- particularly since…
Local dependence random graph models are a class of block models for network data which allow for dependence among edges under a local dependence assumption defined around the block structure of the network. Since being introduced by…
We show that for any $\Delta \geq 3$, there is no bound computable from $(\varepsilon, r)$ on the size of a graph required to approximate a graph of maximum degree at most $\Delta$ up to $\varepsilon$ error in $r$-neighborhood statistics.…
Goemans and Williamson proposed a randomized rounding algorithm for the MAX-CUT problem with a 0.878 approximation bound in expectation. The 0.878 approximation bound remains the best-known approximation bound for this APX-hard problem.…
The following question is due to Chatterjee and Varadhan (2011). Fix $0<p<r<1$ and take $G\sim G(n,p)$, the Erd\H{o}s-R\'enyi random graph with edge density $p$, conditioned to have at least as many triangles as the typical $G(n,r)$. Is $G$…
The spectral radius {\rho}(G) of a digraph G is the maximum modulus of the eigenvalues of its adjacency matrix. We present bounds on {\rho}(G) that are often tighter and are applicable to a larger class of digraphs than previously reported…
A celebrated result of Alon from 1993 states that any $d$-regular graph on $n$ vertices (where $d=O(n^{1/9})$) has a bisection with at most $\frac{dn}{2}(\frac{1}{2}-\Omega(\frac{1}{\sqrt{d}}))$ edges, and this is optimal. Recently, this…
In communication field, an important issue is to group users and base stations to as many as possible subnetworks satisfying certain interference constraints. These problems are usually formulated as a graph partition problems which…
Bounded-size rules are dynamic random graph processes which incorporate limited choice along with randomness in the evolution of the system. One starts with the empty graph and at each stage two edges are chosen uniformly at random. One of…
We derive attainable upper bounds on the algebraic connectivity (spectral gap) of a regular graph in terms of its diameter and girth. This bound agrees with the well-known Alon-Boppana-Friedman bound for graphs of even diameter, but is an…
This paper is devoted to the distributed complexity of finding an approximation of the maximum cut in graphs. A classical algorithm consists in letting each vertex choose its side of the cut uniformly at random. This does not require any…
For any fixed simple graph $H=(V,E)$ and any fixed $u>0$, we establish the leading order of the exponential rate function for the probability that the number of copies of $H$ in the Erd\H{o}s--R\'enyi graph $G(n,p)$ exceeds its expectation…
For the set of graphs with a given degree sequence, consisting of any number of $2's$ and $1's$, and its subset of bipartite graphs, we characterize the optimal graphs who maximize and minimize the number of $m$-matchings. We find the…
One-shot coupling is a method of bounding the convergence rate between two copies of a Markov chain in total variation distance, which was first introduced by Roberts and Rosenthal and generalized by Madras and Sezer. The method is divided…