32 citations · 117 across the 58 of their papers we have counts for
53 papers · 1 filter
Cooling graph products
Anthony Bonato, MacKenzie Carr, Caleb Jones +2
The cooling number measures the speed at which a slow-moving influence or contagion spreads on a graph. In this paper, we investigate the cooling number of four classical graph pro…
Between burning and cooling: liminal burning on graphs
Anthony Bonato, Trent G. Marbach, John Marcoux +1
Liminal burning generalizes both the burning and cooling processes in graphs. In -liminal burning, a Saboteur reveals -sets of vertices in each round, with the goal of extend…
Hypergraph burning, matchings, and zero forcing
Anthony Bonato, Caleb Jones, Trent G. Marbach +2
Lazy burning is a recently introduced variation of burning where only one set of vertices is chosen to burn in the first round. In hypergraphs, lazy burning spreads when all but on…
How to burn a Latin square
Anthony Bonato, Caleb Jones, Trent G. Marbach +1
We investigate the lazy burning process for Latin squares by studying their associated hypergraphs. In lazy burning, a set of vertices in a hypergraph is initially burned, and that…
The isoperimetric peak of complete trees
Anthony Bonato, Lazar Mandic, Trent G. Marbach +1
We give exact values and bounds on the isoperimetric peak of complete trees, improving on known results. For the complete -ary tree of depth , if , then we find that…
Locally finite graphs and their localization numbers
Anthony Bonato, Florian Lehner, Trent G. Marbach +1
We study the Localization game on locally finite graphs trees, where each of the countably many vertices have finite degree. In contrast to the finite case, we construct a locally…
How to cool a graph
Anthony Bonato, Trent G. Marbach, Holden Milne +1
We introduce a new graph parameter called the cooling number, inspired by the spread of influence in networks and its predecessor, the burning number. The cooling number measures t…
The -visibility Localization Game
Anthony Bonato, Trent G. Marbach, John Marcoux +1
We study a variant of the Localization game in which the cops have limited visibility, along with the corresponding optimization parameter, the -visibility localization number $…
The one-visibility Localization game
Anthony Bonato, Trent G. Marbach, Michael Molnar +1
We introduce a variant of the Localization game in which the cops only have visibility one, along with the corresponding optimization parameter, the one-visibility localization num…
The Localization Game on Directed Graphs
Anthony Bonato, Ryan Cushman, Trent G. Marbach +1
In the Localization game played on graphs, a set of cops uses distance probes to identify the location of an invisible robber. We present an extension of the game and its main para…
On Meyniel extremal families of graphs
Anthony Bonato, Ryan Cushman, Trent G. Marbach
We provide new constructions of Meyniel extremal graphs, which are families of graphs with the conjectured largest asymptotic cop number. Using spanning subgraphs, we prove that th…
An improved bound on the burning number of graphs
Anthony Bonato, Shahin Kamali
The burning number conjecture states that the burning number of a connected graph is at most While the conjecture is unresolved, Land and Lu proved that t…
Improved pyrotechnics : Closer to the burning graph conjecture
Paul Bastide, Marthe Bonamy, Anthony Bonato +4
The Burning Number Conjecture claims that for every connected graph of order its burning number satisfies While the conjecture remains o…
Pursuit-evasion games on latin square graphs
Shreya Ahirwar, Anthony Bonato, Leanna Gittins +3
We investigate various pursuit-evasion parameters on latin square graphs, including the cop number, metric dimension, and localization number. The cop number of latin square graphs…
The localization capture time of a graph
Natalie C. Behague, Anthony Bonato, Melissa A. Huggan +2
The localization game is a pursuit-evasion game analogous to Cops and Robbers, where the robber is invisible and the cops send distance probes in an attempt to identify the locatio…
Progress on the localization number of a graph
Anthony Bonato, Melissa A. Huggan, Trent G. Marbach
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…
The game of Flipping Coins
Anthony Bonato, Melissa A. Huggan, Richard J. Nowakowski
We consider Flipping Coins, a partizan version of the impartial game Turning Turtles, played on lines of coins. We show the values of this game are numbers, and these are found by…
A survey of graph burning
Anthony Bonato
Graph burning is a deterministic, discrete-time process that models how influence or contagion spreads in a graph. Associated to each graph is its burning number, which is a parame…
The localization number and metric dimension of graphs of diameter 2
Anthony Bonato, Melissa A. Huggan, Trent Marbach
We consider the localization number and metric dimension of certain graphs of diameter , focusing on families of Kneser graphs and graphs without 4-cycles. For the Kneser graphs…
The localization number of designs
Anthony Bonato, Melissa A. Huggan, Trent Marbach
We study the localization number of incidence graphs of designs. In the localization game played on a graph, the cops attempt to determine the location of an invisible robber via d…
Improved Bounds for Burning Fence Graphs
Anthony Bonato, Sean English, Bill Kay +1
Graph burning studies how fast a contagion, modeled as a set of fires, spreads in a graph. The burning process takes place in synchronous, discrete rounds. In each round, a fire br…
The Iterated Local Model for Social Networks
Anthony Bonato, Huda Chuangpishit, Sean English +2
On-line social networks, such as in Facebook and Twitter, are often studied from the perspective of friendship ties between agents in the network. Adversarial ties, however, also p…
Optimizing the trade-off between number of cops and capture time in Cops and Robbers
Anthony Bonato, Jane Breen, Boris Brimkov +6
The cop throttling number of a graph for the game of Cops and Robbers is the minimum of , where is the number of cops and is the minimu…
A Sublinear Bound on the Cop Throttling Number of a Graph
Anthony Bonato, Sean English
We provide a sublinear bound on the cop throttling number of a connected graph. Related to the graph searching game Cops and Robbers, the cop throttling number, written $\mathrm{th…