18 citations · 39 across the 14 of their papers we have counts for
17 papers
Achievable Burning Densities of Growing Grids
Jordan Barrett, Karen Gunderson, JD Nir +1
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 o…
Induced forests in some distance-regular graphs
Karen Gunderson, Karen Meagher, Joy Morris +1
In this article, we study the order and structure of the largest induced forests in some families of graphs. First we prove a variation of the ratio bound that gives an upper bound…
Adversarial graph burning densities
Karen Gunderson, William Kellough, JD Nir +1
Graph burning is a discrete-time process that models the spread of influence in a network. Vertices are either burning or unburned, and in each round, a burning vertex causes all o…
The oriented chromatic number of random graphs of bounded degree
Karen Gunderson, JD Nir
The chromatic number of the random graph has long been studied and has inspired several landmark results. In the case where , Achlioptas and Naor showed…
Burning the plane: densities of the infinite Cartesian grid
Anthony Bonato, Karen Gunderson, Amy Shaw
Graph burning is a discrete-time process on graphs, where vertices are sequentially burned, and burned vertices cause their neighbours to burn over time. We consider extremal prope…
Minimum degree conditions for small percolating sets in bootstrap percolation
Karen Gunderson
The -neighbour bootstrap process is an update rule for the states of vertices in which `uninfected' vertices with at least `infected' neighbours become infected and a set of…
Tournaments, 4-uniform hypergraphs, and an exact extremal result
Karen Gunderson, Jason Semeraro
We consider -uniform hypergraphs with the maximum number of hyperedges subject to the condition that every set of vertices spans either or exactly hyperedges and giv…
A sharp threshold for a modified bootstrap percolation with recovery
Tom Coker, Karen Gunderson
Bootstrap percolation is a type of cellular automaton on graphs, introduced as a simple model of the dynamics of ferromagnetism. Vertices in a graph can be in one of two states: `h…
Positive independence densities of finite rank countable hypergraphs are achieved by finite hypergraphs
Paul Balister, Béla Bollobás, Karen Gunderson
The independence density of a finite hypergraph is the probability that a subset of vertices, chosen uniformly at random contains no hyperedges. Independence densities can be gener…
Random Geometric Graphs and Isometries of Normed Spaces
Paul Balister, Béla Bollobás, Karen Gunderson +2
Given a countable dense subset of a finite-dimensional normed space , and , we form a random graph on by joining, independently and with probability , each pai…
The time of graph bootstrap percolation
Karen Gunderson, Sebastian Koch, Michał Przykucki
Graph bootstrap percolation, introduced by Bollobás in 1968, is a cellular automaton defined as follows. Given a "small" graph and a "large" graph , in c…
Limited packings of closed neighbourhoods in graphs
Paul N. Balister, Béla Bollobás, Karen Gunderson
The k-limited packing number, , of a graph , introduced by Gallant, Gunther, Hartnell, and Rall, is the maximum cardinality of a set of vertices of such that eve…
Bounding the Number of Hyperedges in Friendship -Hypergraphs
Karen Gunderson, Natasha Morrison, Jason Semeraro
For , an -uniform hypergraph is called a friendship -hypergraph if every set of vertices has a unique 'friend' - that is, there exists a unique vertex $x \no…
Almost Separable Matrices
Matthew Aldridge, Leonardo Baldassini, Karen Gunderson
An matrix with column supports is -separable if the disjunctions are all distinct over all sets $\mathcal{K…
Random-step Markov processes
Neal Bushaw, Karen Gunderson, Steven Kalikow
We explore two notions of stationary processes. The first is called a random-step Markov process in which the stationary process of states, has a station…
Lower bounds for bootstrap percolation on Galton-Watson trees
Karen Gunderson, Michał Przykucki
Bootstrap percolation is a cellular automaton modelling the spread of an `infection' on a graph. In this note, we prove a family of lower bounds on the critical probability for …
Bootstrap percolation on Galton-Watson trees
Béla Bollobás, Karen Gunderson, Cecilia Holmgren +2
Bootstrap percolation is a type of cellular automaton which has been used to model various physical phenomena, such as ferromagnetism. For each natural number , the -neighbou…