13 citations · 19 across the 15 of their papers we have counts for
26 papers · 1 filter
Cost-Benefit Analysis for PMU Placement in Power Grids
Beth Bjorkman, Sean English, Johnathan Koch
Power domination is a graph-theoretic model for the observance of a power grid using phasor measurement units (PMUs). There are many costs associated with the installation of a PMU…
Saturation Numbers for Berge Cliques
Sean English, Jürgen Kritschgau, Mina Nahvi +1
Let be a graph and be a hypergraph, both embedded on the same vertex set. We say is a Berge- if there exists a bijection $ϕ:E(F)\to E(\mathcal{H}…
A random coloring process gives improved bounds for the Erdős-Gyárfás problem on generalized Ramsey numbers
Patrick Bennett, Andrzej Dudek, Sean English
The Erdős-Gyárfás number is the smallest number of colors needed to color the edges of the complete graph so that all of its -clique spans at least colors…
Rainbow Connection for Complete Multipartite Graphs
Igor Araujo, Kareem Benaissa, Richard Bi +3
A path in an edge-colored graph is said to be rainbow if no color repeats on it. An edge-colored graph is said to be rainbow -connected if every pair of vertices is connected by…
Saturation for the -uniform loose -cycle
Sean English, Alexandr Kostochka, Dara Zirlin
Let and be -uniform hypergraphs. We say is -saturated if does not contain a subgraph isomorphic to , but does for any hyperedge . The…
Chasing the Threshold Bias of the 3-AP Game
Albert Cao, Felix Christian Clemen, Sean English +4
In a Maker-Breaker game there are two players, Maker and Breaker, where Maker wins if they create a specified structure while Breaker wins if they prevent Maker from winning indefi…
Linear Bounds for Cycle-free Saturation Games
Sean English, Tomáš Masařík, Grace McCourt +3
Given a family of graphs , we define the -saturation game as follows. Two players alternate adding edges to an initially empty graph on vertices, with…
Low Diameter Monochromatic Covers of Complete Multipartite Graphs
Sean English, Connor Mattes, Grace McCourt +1
Let the diameter cover number, , denote the least integer such that under any -coloring of the edges of the graph , there exists a collection of monochromat…
Lower bounds on the Erdős-Gyárfás problem via color energy graphs
József Balogh, Sean English, Emily Heath +1
Given positive integers and , a -coloring of the complete graph is an edge-coloring in which every -clique receives at least colors. Erdős and Shelah pos…
Firefighting on the Hexagonal Grid and on Infinite Trees
Alexander Dean, Sean English, Tongyun Huang +4
The firefighter problem with firefighters on an infinite graph is an iterative graph process, defined as follows: Suppose a fire breaks out at a given vertex on…
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…
Localization Game for Random Graphs
Andrzej Dudek, Sean English, Alan Frieze +2
We consider the localization game played on graphs in which a cop tries to determine the exact location of an invisible robber by exploiting distance probes. The corresponding grap…
Probabilistic Zero Forcing on Random Graphs
Sean English, Calum MacRury, Pawel Pralat
Zero forcing is a deterministic iterative graph coloring process in which vertices are colored either blue or white, and in every round, any blue vertices that have a single white…
On the weight of Berge--free hypergraphs
Sean English, Dániel Gerbner, Abhishek Methuku +1
For a graph , we say a hypergraph is a Berge- if it can be obtained from by replacing each edge of with a hyperedge containing it. A hypergraph is Berge--free if i…
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…
Zero Forcing Number of Random Regular Graphs
Deepak Bal, Patrick Bennett, Sean English +2
The zero forcing process is an iterative graph colouring process in which at each time step a coloured vertex with a single uncoloured neighbour can force this neighbour to become…
Nearly-Regular Hypergraphs and Saturation of Berge Stars
Bethany Austhof, Sean English
Given a graph , we say a -uniform hypergraph on the same vertex set contains a Berge- if there exists an injection such that for each…
Weighted Turan Problems with Applications
Patrick Bennett, Sean English, Maria Talanda-Fisher
Suppose the edges of are assigned weights by a weight function . We define the {\em weighted extremal number} \[ \mathrm{ex}(n,w,F):=\max\{w(G)\mid G\subseteq K_n,\text{ a…
Linearity of Saturation for Berge Hypergraphs
Sean English, Dániel Gerbner, Abhishek Methuku +1
For a graph , we say a hypergraph is Berge- if it can be obtained from be replacing each edge of with a hyperedge containing it. We say a hypergraph is Berge--…
A random variant of the game of plates and olives
Andrzej Dudek, Sean English, Alan Frieze
The game of plates and olives was originally formulated by Nicolaescu and encodes the evolution of the topology of the sublevel sets of Morse functions. We consider a random varian…
The zero forcing polynomial of a graph
Kirk Boyer, Boris Brimkov, Sean English +5
Zero forcing is an iterative graph coloring process, where given a set of initially colored vertices, a colored vertex with a single uncolored neighbor causes that neighbor to beco…
Saturation of Berge Hypergraphs
Sean English, Nathan Graber, Pamela Kirkpatrick +2
Given a graph , a hypergraph is a Berge- if it can be obtained by expanding each edge in to a hyperedge containing it. A hypergraph is Berge--saturated if does…