Related papers: Burning graphs - a probabilistic perspective
Burning and cooling are diffusion processes on graphs in which burned (or cooled) vertices spread to their neighbors with a new source picked at discrete time steps. In burning, the one tries to burn the graph as fast as possible, while in…
The burning number $b(G)$ of a graph $G$ is the smallest number of turns required to burn all vertices of a graph if at every turn a new fire is started and existing fires spread to all adjacent vertices. The Burning Number Conjecture of…
The Burning Number Conjecture claims that for every connected graph $G$ of order $n,$ its burning number satisfies $b(G) \le \lceil \sqrt{n} \rceil.$ While the conjecture remains open, we prove that it is asymptotically true when the order…
By means of a binary visibility graph, we present a novel method to study random binary sequences. The behavior of the some topological properties of the binary visibility graph, such as the degree distribution, the clustering coefficient,…
The problem of graph burning was firstly introduced as a model for different processes of social and network interactions. Recently, the authors of the present paper developed methods of algebraic topology for investigation of this problem.…
We introduce Graph Neural Processes (GNP), inspired by the recent work in conditional and latent neural processes. A Graph Neural Process is defined as a Conditional Neural Process that operates on arbitrary graph data. It takes features of…
Consider an information diffusion process on a graph $G$ that starts with $k>0$ burnt vertices, and at each subsequent step, burns the neighbors of the currently burnt vertices, as well as $k$ other unburnt vertices. The \emph{$k$-burning…
Graph burning is a graph process that models the spread of social contagion. Initially, all the vertices of a graph $G$ are unburnt. At each step, an unburnt vertex is put on fire and the fire from burnt vertices of the previous step…
We investigate the linear chromatic number $\chi_{\text{lin}}(G(n,p))$ of the binomial random graph $G(n,p)$ on $n$ vertices in which each edge appears independently with probability $p=p(n)$. For dense random graphs ($np \to \infty$ as $n…
Graph burning is a process of information spreading through the network by an agent in discrete steps. The problem is to find an optimal sequence of nodes which have to be given information so that the network is covered in least number of…
We introduce a family of graph parameters, called induced multipartite graph parameters, and study their computational complexity. First, we consider the following decision problem: an instance is an induced multipartite graph parameter $p$…
In the branch of mathematics known as graph theory, graphs are considered as a set of points, called vertices, with connections between these points, called edges. The purpose of this paper is to study mappings between two graphs that have…
We highlight new results on the localization number of a graph, a parameter derived from the localization graph searching game. After introducing the game and providing an overview of existing results, we describe recent results on the…
In this paper we introduce a novel polynomial-time algorithm to compute graph invariants based on the modified random walk idea on graphs. However not proved to be a full graph invariant by now, our method gives the right answer for the…
Random planar graphs have been the subject of much recent work. Many basic properties of the standard uniform random planar graph P_{n}, by which we mean a graph chosen uniformly at random from the set of all planar graphs with vertex set…
Traditionally, graph neural networks have been trained using a single observed graph. However, the observed graph represents only one possible realization. In many applications, the graph may encounter uncertainties, such as having…
The burning number of a graph is the minimal number of steps that are needed to burn all of its vertices, with the following burning procedure: at each step, one can choose a point to set on fire, and the fire propagates constantly at unit…
Let P_{n,d,D} denote the graph taken uniformly at random from the set of all labelled planar graphs on {1,2,...,n} with minimum degree at least d(n) and maximum degree at most D(n). We use counting arguments to investigate the probability…
One of the hot topics in machine learning is the field of GNN. The complexity of graph data has imposed significant challenges on existing machine learning algorithms. Recently, many studies on extending deep learning approaches for graph…
The burning and forcing processes are both instances of propagation processes on graphs that are commonly used to model real-world spreading phenomena. The contribution of this paper is two-fold. We first establish a connection between…