1 citations · 8 across the 24 of their papers we have counts for
32 papers
Burning Steiner triple systems
Andrea C. Burgess, Peter H. Danziger, Caleb W. Jones +2
Graph burning is a round-based process which can be viewed as a discrete one-player game that models the spread of influence throughout a network. Extending this process to hypergr…
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…
The Iterated Local Model for tournaments
Anthony Bonato, MacKenzie Carr, Ketan Chaudhary +2
Transitivity is a central, generative principle in social and other complex networks, capturing the tendency for two nodes with a common neighbor to form a direct connection. We pr…
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…
Cuts, Cats, and Complete Graphs
Rylo Ashmore, Danny Dyer, Trent Marbach +1
We introduce the game of Cat Herding, where an omnipresent herder slowly cuts down a graph until an evasive cat player has nowhere to go. The number of cuts made is the score of a…
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…
Tic-Tac-Toe on Designs
Peter Danziger, Melissa A. Huggan, Rehan Malik +1
We consider playing the game of Tic-Tac-Toe on block designs BIBD() and transversal designs TD(). Players take turns choosing points and the first player to complete…
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…
Iterative models for complex networks formed by extending cliques
Anthony Bonato, Ryan Cushman, Trent G. Marbach +1
We consider a new model for complex networks whose underlying mechanism is extending dense subgraphs. In the frustum model, we iteratively extend cliques over discrete-time steps.…
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…
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…
Subgraph Games in the Semi-Random Graph Process and Its Generalization to Hypergraphs
Natalie C. Behague, Trent G. Marbach, Pawel Pralat +1
The semi-random graph process is a single-player game that begins with an empty graph on vertices. In each round, a vertex is presented to the player independently and unif…
Rainbow Thresholds
Tolson Bell, Alan Frieze, Trent G. Marbach
We extend a recent breakthrough result relating expectation thresholds and actual thresholds to include some rainbow versions.
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 iterated local transitivity model for hypergraphs
Natalie C. Behague, Anthony Bonato, Melissa A. Huggan +2
Complex networks are pervasive in the real world, capturing dyadic interactions between pairs of vertices, and a large corpus has emerged on their mining and modeling. However, man…
Tight Bounds on the Probabilistic Zero Forcing on Hypercubes and Grids
Natalie C. Behague, Trent Marbach, Pawel Pralat
Zero forcing is a deterministic iterative graph colouring process in which vertices are coloured either blue or white, and in every round, any blue vertices that have a single whit…
Tic-Tac-Toe on an Affine Plane of order 4
Peter Danziger, Melissa A. Huggan, Rehan Malik +1
The game of tic-tac-toe is well known. In particular, in its classic version it is famous for being unwinnable by either player. While classically it is played on a grid, it is nat…