Related papers: Burning graphs - a probabilistic perspective
Inspired by a concept in comparative genomics, we investigate properties of randomly chosen members of G_1(m,n,t), the set of bipartite graphs with $m$ left vertices, n right vertices, t edges, and each vertex of degree at least one. We…
We study random graphs with latent geometric structure, where the probability of each edge depends on the underlying random positions corresponding to the two endpoints. We focus on the setting where this conditional probability is a…
Wildfire forecasting is notoriously hard due to the complex interplay of different factors such as weather conditions, vegetation types and human activities. Deep learning models show promise in dealing with this complexity by learning…
We consider a constrained version of the shortest path problem on the complete graphs whose edges have independent random lengths and costs. We establish the asymptotic value of the minimum length as a function of the cost-budget within a…
Given graphs as input, Graph Neural Networks (GNNs) support the inference of nodes, edges, attributes, or graph properties. Graph Rewriting investigates the rule-based manipulation of graphs to model complex graph transformations. We…
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…
Recently, techniques for applying convolutional neural networks to graph-structured data have emerged. Graph convolutional neural networks (GCNNs) have been used to address node and graph classification and matrix completion. Although the…
Threshold graphs are recursive deterministic network models that have been proposed for describing certain economic and social interactions. One drawback of this graph family is that it has limited generative attachment rules. To mitigate…
We study the escape probability problem in random walks over graphs. Given vertices, $s,t,$ and $p$, the problem asks for the probability that a random walk starting at $s$ will hit $t$ before hitting $p$. Such probabilities can be…
A Burling graph is an induced subgraph of some graph in Burling's construction of triangle-free high-chromatic graphs. Equivalently, a Burling graph is a graph that admits a so-called strict frame representation. We provide a…
A random geometric graph $G_n$ is given by picking $n$ vertices in $\mathbb{R}^d$ independently under a common bounded probability distribution, with two vertices adjacent if and only if their $l^p$-distance is at most $r_n$. We investigate…
Path graphs are intersection graphs of paths in a tree. We start from the characterization of path graphs by Monma and Wei [C.L.~Monma,~and~V.K.~Wei, Intersection Graphs of Paths in a Tree, J. Combin. Theory Ser. B, 41:2 (1986) 141--181]…
We study the Hamiltonicity of the following model of a random graph. Suppose that we partition [n] into V_1,V_2,...,V_k and add edge {x,y} to our graph with probability p if there exists i such that x,y\in V_i. Otherwise, we add the edge…
We introduce a new notation for representing labeled regular bipartite graphs of arbitrary degree. Several enumeration problems for labeled and unlabeled regular bipartite graphs have been introduced. A general algorithm for enumerating all…
The vertex coloring problem to find chromatic numbers is known to be unsolvable in polynomial time. Although various algorithms have been proposed to efficiently compute chromatic numbers, they tend to take an enormous amount of time for…
We introduce a new graph invariant that measures fractional covering of a graph by cuts. Besides being interesting in its own right, it is useful for study of homomorphisms and tension-continuous mappings. We study the relations with…
We develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes. Our approach generalizes the usual (co)variance to the setting of…
Chromatic polynomials and related graph invariants are central objects in both graph theory and statistical physics. Computational difficulties, however, have so far restricted studies of such polynomials to graphs that were either very…
Consider the setting of \emph{randomly weighted graphs}, namely, graphs whose edge weights are chosen independently according to probability distributions with finite support over the non-negative reals. Under this setting, properties of…
Knowledge graphs have emerged to be promising datastore candidates for context augmentation during Retrieval Augmented Generation (RAG). As a result, techniques in graph representation learning have been simultaneously explored alongside…