Related papers: Random graphs from structured classes

We introduce a new class of countably infinite random geometric graphs, whose vertices are points in a metric space, and vertices are adjacent independently with probability p if the metric distance between the vertices is below a given…

Consider $n$ points distributed uniformly in $[0,1]^d$. Form a graph by connecting two points if their mutual distance is no greater than $r(n)$. This gives a random geometric graph, $\gnrn$, which is connected for appropriate $r(n)$. We…

Let $C_{n,g}$ be the number of rooted cubic maps with $2n$ vertices on the orientable surface of genus $g$. We show that the sequence $(C_{n,g}:g\ge 0)$ is asymptotically normal with mean and variance asymptotic to $(1/2)(n-\ln n)$ and…

k-connectivity of random graphs is a fundamental property indicating reliability of multi-hop wireless sensor networks (WSN). WSNs comprising of sensor nodes with limited power resources are modeled by random graphs with unreliable nodes,…

In this thesis, which is supervised by Dr. David Penman, we examine random interval graphs. Recall that such a graph is defined by letting $X_{1},\ldots X_{n},Y_{1},\ldots Y_{n}$ be $2n$ independent random variables, with uniform…

Network-topology inference from (vertex) signal observations is a prominent problem across data-science and engineering disciplines. Most existing schemes assume that observations from all nodes are available, but in many practical…

Augustine et al. [DISC 2022] initiated the study of distributed graph algorithms in the presence of Byzantine nodes in the congested clique model. In this model, there is a set $B$ of Byzantine nodes, where $|B|$ is less than a third of the…

We find new upper bounds on the size of a minimum totally dominating set for random regular graphs and for regular graphs with large girth. These bounds are obtained through the analysis of a local algorithm using a method due to Hoppen and…

The H-free process, for some fixed graph H, is the random graph process defined by starting with an empty graph on n vertices and then adding edges one at a time, chosen uniformly at random subject to the constraint that no H subgraph is…

We study the structure of the asymptotic expansion of the probability that a combinatorial object is connected. We show that the coefficients appearing in those asymptotics are integers and can be interpreted as the counting sequences of…

We prove that a graph G is asymptotically isomorphic to the ray if and only if G is uniformly spherically bounded and is of bounded local degrees. This problem arouse in combinatorics and was posed in [3] (Problem 10.1).

We propose to study the problem of few shot graph classification in graph neural networks (GNNs) to recognize unseen classes, given limited labeled graph examples. Despite several interesting GNN variants being proposed recently for node…

Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such…

In an earlier paper the authors proved that limits of convergent graph sequences can be described by various structures, including certain 2-variable real functions called graphons, random graph models satisfying certain consistency…

Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…

Let $G$ be a dense graph with good expansion properties and not too close to being bipartite. Let $\boldsymbol d$ be a graphical degree sequence. Under very weak conditions, we find the number of subgraphs of $G$ with degree sequence…

We prove that the class of chordal graphs is easily testable in the following sense. There exists a constant $c>0$ such that, if adding/removing at most $\epsilon n^2$ edges to a graph $G$ with $n$ vertices does not make it chordal, then a…

For any positive edge density $p$, a random graph in the Erd\H{o}s-Renyi $G_{n,p}$ model is connected with non-zero probability, since all edges are mutually independent. We consider random graph models in which edges that do not share…

Suppose $G$ is a graph with degrees bounded by $d$, and one needs to remove more than $\epsilon n$ of its edges in order to make it planar. We show that in this case the statistics of local neighborhoods around vertices of $G$ is far from…

Quasi-random graphs can be informally described as graphs whose edge distribution closely resembles that of a truly random graph of the same edge density. Recently, Shapira and Yuster proved the following result on quasi-randomness of…