JD Nir

activity

20212026

most citedEvery graph is eventually Turán-good

9 citations · 12 across the 11 of their papers we have counts for

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Showing math.COShow all

12 papers · 1 filter

math.CO2026

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…

math.CO2025

Hoffman-London graphs: When paths minimize $H$ -colorings among trees

David Galvin, Phillip Marmorino, Emily McMillon +2

Given a graph $G$ and a target graph $H$ , an $H$ -coloring of $G$ is an adjacency-preserving vertex map from $G$ to $H$ . The number of $H$ -colorings of $G$ , $hom (G, H)$ , has been st…

math.CO2025

Long paths need not minimize $H$ -colorings among trees

David Galvin, Emily McMillon, JD Nir +1

Given a graph $G$ and a target graph $H$ , an $H$ -coloring of $G$ is an adjacency-preserving vertex map from $G$ to $H$ . By appropriate choice of $H$ , these colorings can express, f…

math.CO2024

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…

math.CO2023

The $k$ -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 $k$ -visibility localization number $…

math.CO2023★ 1 cited

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…

math.CO2023★ 1 cited

A localized approach to generalized Turán problems

Rachel Kirsch, JD Nir

Generalized Turán problems ask for the maximum number of copies of a graph $H$ in an $n$ -vertex, $F$ -free graph, denoted by ex $(n, H, F)$ . We show how to extend the new, localized ap…

math.CO2022★ 1 cited

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…

math.CO2022★ 9 cited

Every graph is eventually Turán-good

Natasha Morrison, JD Nir, Sergey Norin +2

Let $H$ be a graph. We show that if $r$ is large enough as a function of $H$ , then the $r$ -partite Turán graph maximizes the number of copies of $H$ among all $K_{r + 1}$ -free graphs…

math.CO2022

The oriented chromatic number of random graphs of bounded degree

Karen Gunderson, JD Nir

The chromatic number of the random graph $G (n, p)$ has long been studied and has inspired several landmark results. In the case where $p = d / n$ , Achlioptas and Naor showed…

math.CO2021

The chromatic number of random lifts of complete graphs

JD Nir, Xavier Pérez Giménez

An $n$ -lift of a graph $G$ is a graph from which there is an $n$ -to- $1$ covering map onto $G$ . Amit, Linial, and Matou\v sek (2002) raised the question of whether the chromatic num…

math.CO2021

Paths of Length Three are $K_{r + 1}$ -Turán Good

Kyle Murphy, JD Nir

The generalized Turán problem $e x t (n, T, F)$ is to determine the maximal number of copies of a graph $T$ that can exist in an $F$ -free graph on $n$ vertices. Recently, Gerbner and Pa…