9 citations · 12 across the 11 of their papers we have counts for
12 papers · 1 filter
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…
Hoffman-London graphs: When paths minimize -colorings among trees
David Galvin, Phillip Marmorino, Emily McMillon +2
Given a graph and a target graph , an -coloring of is an adjacency-preserving vertex map from to . The number of -colorings of , , has been st…
Long paths need not minimize -colorings among trees
David Galvin, Emily McMillon, JD Nir +1
Given a graph and a target graph , an -coloring of is an adjacency-preserving vertex map from to . By appropriate choice of , these colorings can express, f…
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…
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…
A localized approach to generalized Turán problems
Rachel Kirsch, JD Nir
Generalized Turán problems ask for the maximum number of copies of a graph in an -vertex, -free graph, denoted by ex. We show how to extend the new, localized ap…
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…
Every graph is eventually Turán-good
Natasha Morrison, JD Nir, Sergey Norin +2
Let be a graph. We show that if is large enough as a function of , then the -partite Turán graph maximizes the number of copies of among all -free graphs…
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…
The chromatic number of random lifts of complete graphs
JD Nir, Xavier Pérez Giménez
An -lift of a graph is a graph from which there is an -to- covering map onto . Amit, Linial, and Matou\v sek (2002) raised the question of whether the chromatic num…
Paths of Length Three are -Turán Good
Kyle Murphy, JD Nir
The generalized Turán problem is to determine the maximal number of copies of a graph that can exist in an -free graph on vertices. Recently, Gerbner and Pa…