60 citations · 178 across the 36 of their papers we have counts for
10 papers · 1 filter
Leaky forcing and resilience of Cartesian products of
Rebekah Herrman, Grace Wisdom
Zero forcing is a process on a graph in which a set of initially colored vertices,, can color their neighbors according to the color change rule. T…
Bootstrap percolation and -hull number in direct products of graphs
Boštjan Brešar, Jaka Hedžet, Rebekah Herrman
The -neighbor bootstrap percolation is a graph infection process based on the update rule by which a vertex with infected neighbors becomes infected. We say that an initial…
A Proof of the Grundy domination strong product conjecture
Rebekah Herrman, Stephen G. Z. Smith
The Grundy domination number of a simple graph is the length of the longest sequence of unique vertices , , that satisfies the proper…
Extending Grundy domination to -Grundy domination
Rebekah Herrman, Stephen G. Z. Smith
The Grundy domination number of a graph is the length of the longest sequence of unique vertices satisfying $N[v_i] \setminus \cup_{j=1}^{i-1}N…
Upper bound for the -leaky forcing number of and -leaky forcing number of
Rebekah Herrman
Leaky-forcing is a recently introduced variant of zero-forcing that has been studied for families of graphs including paths, cycles, wheels, grids, and trees. In this paper, we ext…
On the length of L-Grundy sequences
Rebekah Herrman, Stephen G. Z. Smith
An L- sequence of a graph is a sequence of distinct vertices such that . The length of the lo…
Capture times in the Bridge-burning Cops and Robbers game
Rebekah Herrman, Peter van Hintum, Stephen G. Z. Smith
In this paper, we consider a variant of the cops and robbers game on a graph, introduced by Kinnersley and Peterson, in which every time the robber uses an edge, it is removed from…
The Eternal Game Chromatic Number of Random Graphs
Vojtěch Dvořák, Rebekah Herrman, Peter van Hintum
The eternal graph colouring problem, recently introduced by Klostermeyer and Mendoza, is a version of the graph colouring game, where two players take turns properly colouring a gr…
(t,r) broadcast domination in the infinite grid
Rebekah Herrman, Peter van Hintum
The broadcast domination number of a graph , , is a generalization of the domination number of a graph. is the minimal number of towers needed,…
Uniform Bounds for Non-negativity of the Diffusion Game
Andrew Carlotti, Rebekah Herrman
We study a variant of the chip-firing game called the diffusion game. In the diffusion game, we begin with some integer labelling of the vertices of a graph, interpreted as a numbe…