Related papers: A survey of graph burning
Brushing of graphs is a graph searching process in which the searching agents are called brushes. We focus on brushing directed graphs based on a new model in which the brushes can only travel in the same direction as the orientation of the…
In this paper we study the graph parameter of burning number, introduced by Bonato, Janssen, and Roshanbin (2014). We are particular interested in determining the burning number of Circulant graphs. In this paper, we find upper and lower…
We consider the problem of controlling a partially-observed dynamic process on a graph by a limited number of interventions. This problem naturally arises in contexts such as scheduling virus tests to curb an epidemic; targeted marketing in…
In this paper we study graph burnings using methods of algebraic topology. We prove that the time function of a burning is a graph map to a path graph. Afterwards, we define a category whose objects are graph burnings and morphisms are…
The burning number of a graph $G$ is the smallest number $b$ such that the vertices of $G$ can be covered by balls of radii $0, 1, \dots, b-1$. As computing the burning number of a graph is known to be NP-hard, even on trees, it is natural…
For a given number of colors, $s$, the guessing number of a graph is the (base $s$) logarithm of the cardinality of the largest family of colorings of the vertex set of the graph such that the color of each vertex can be determined from the…
Bootstrap percolation is a process that is used to model the spread of an infection on a given graph. In the model considered here each vertex is equipped with an individual threshold. As soon as the number of infected neighbors exceeds…
Graph coloring is a problem with varied applications in industry and science such as scheduling, resource allocation, and circuit design. The purpose of this paper is to establish if a new gradient based iterative solver framework known as…
Flame graphs are a popular way of representing profiling data. In this paper we propose a possible mathematical definition of flame graphs. In doing so, we gain some interesting algebraic properties almost for free, which in turn allow us…
Graph coloring is fundamental to distributed computing. We give the first general treatment of the coloring of virtual graphs, where the graph $H$ to be colored is locally embedded within the communication graph $G$. Besides generalizing…
Given a graph $G=(V,E)$, the problem of \gb{} is to find a sequence of nodes from $V$, called burning sequence, in order to burn the whole graph. This is a discrete-step process, in each step an unburned vertex is selected as an agent to…
Graph burning is motivated by the spread of social influence, and the burning number measures the speed of the spread. Given that the smallest burning number among the spanning trees of a graph determines the burning number of a connected…
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…
Graph burning is a discrete-time process on graphs where vertices are sequentially activated and burning vertices cause their neighbours to burn over time. In this work, we focus on a dynamic setting in which the graph grows over time, and…
Probabilistic graphical modeling is a branch of machine learning that uses probability distributions to describe the world, make predictions, and support decision-making under uncertainty. Underlying this modeling framework is an elegant…
Graphs may be used to represent many different problem domains -- a concrete example is that of detecting communities in social networks, which are represented as graphs. With big data and more sophisticated applications becoming widespread…
The popularity of online social networks has enabled rapid dissemination of information. People now can share and consume information much more rapidly than ever before. However, low-quality and/or accidentally/deliberately fake information…
Graph colouring is a combinatorial optimisation problem with applications in several important domains, including sports scheduling, cartography, street map navigation, and timetabling. It is also of significant theoretical interest and a…
Given a social network represented by a graph $G$, we consider the problem of finding a bounded cardinality set of nodes $S$ with the property that the influence spreading from $S$ in $G$ is as large as possible. The dynamics that govern…
The burning process on a graph $G$ starts with a single burnt vertex, and at each subsequent step, burns the neighbors of the currently burnt vertices, as well as one other unburnt vertex. The burning number of $G$ is the smallest number of…