Nathan Warnberg

activity

20142025

most citedRainbow arithmetic progressions

2 citations · 3 across the 11 of their papers we have counts for

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12 papers · 1 filter

math.CO2025

Full classification of anti-van der Waerden numbers of graph products of forests

Zhanar Berikkyzy, Joe Miller, Nathan Warnberg

The anti-van der Waerden number of a graph $G$ is the fewest number of colors needed to guarantee a rainbow $3$ -term arithmetic progression in $G$ , denoted $aw (G, 3)$ …

math.CO2024

Zero Forcing and Vertex Independence Number on Cubic and Subcubic Graphs

Houston Schuerger, Nathan Warnberg, Michael Young

Motivated by a conjecture from the automated conjecturing program TxGraffiti, in this paper the relationship between the zero forcing number, $Z (G)$ , and the vertex independence nu…

math.CO2023

Anti-van der Waerden Numbers of Graph Products with Trees

Zhanar Berikkyzy, Joe Miller, Elizabeth Sprangel +2

Given a graph $G$ , an exact $r$ -coloring of $G$ is a surjective function $c : V (G) \to [1, \dots, r]$ . An arithmetic progression in $G$ of length $j$ with common difference $d$ is a se…

math.CO2023

Rainbow numbers of $[m] \times [n]$ for $x_{1} + x_{2} = x_{3}$

Kean Fallon, Ethan Manhart, Joe Miller +3

Consider the set $[m] \times [n] = {(i, j) : 1 \leq i \leq m, 1 \leq j \leq n}$ and the equation $x_{1} + x_{2} = x_{3}$ , namely $e q$ . The \emph{rainbow number of $[m] \times [n]$ for $e q$ }, d…

math.CO2022

Anti-van der Waerden Numbers of Graph Products of Cycles

Joe Miller, Nathan Warnberg

A $k$ -term arithmetic progression ( $k$ -AP) in a graph $G$ is a list of vertices such that each consecutive pair of vertices is the same distance apart. If $c$ is a coloring functio…

math.CO2020

On leaky forcing and resilience

Joseph S. Alameda, Jürgen Kritschgau, Nathan Warnberg +1

A leak is a vertex that is not allowed to perform a force during the zero forcing process. Leaky forcing was recently introduced as a new variation of zero forcing in order to anal…

math.CO2019

Rainbow Numbers of $Z_{n}$ for $a_{1} x_{1} + a_{2} x_{2} + a_{3} x_{3} = b$

Katie Ansaldi, Houssein El Turkey, Jessica Hamm +3

An exact $r$ -coloring of a set $S$ is a surjective function $c : S \to [r]$ . The rainbow number of a set $S$ for equation $e q$ is the smallest integer $r$ such that every exact $r$ -co…

math.CO2019

Rainbow numbers of $[n]$ for $\sum_{i = 1}^{k - 1} x_{i} = x_{k}$

Kean Fallon, Colin Giles, Hunter Rehm +2

Consider the set ${1, 2, \dots, n} = [n]$ and an equation $e q$ . The rainbow number of $[n]$ for $e q$ , denoted $rb ([n], e q)$ , is the smallest number of colors such that…

math.CO2018

Properties of a $q$ -analogue of zero forcing

Steve Butler, Craig Erickson, Shaun Fallat +6

Zero forcing is a combinatorial game played on a graph where the goal is to start with all vertices unfilled and to change them to filled at minimal cost. In the original variation…

math.CO2018★ 1 cited

Anti-van der Waerden Numbers of Graph Products

Hunter Rehm, Alex Schulte, Nathan Warnberg

In this paper, anti-van der Waerden numbers on Cartesian products of graphs are investigated and a conjecture made by Schulte, et al (see arXiv:1802.01509) is answered. In particul…

math.CO2018

Anti-van der Waerden numbers on Graphs

Zhanar Berikkyzy, Alex Schulte, Elizabeth Sprangel +3

In this paper arithmetic progressions on the integers and the integers modulo n are extended to graphs. This allows for the definition of the anti-van der Waerden number of a graph…

math.CO2014★ 2 cited

Rainbow arithmetic progressions

Steve Butler, Craig Erickson, Leslie Hogben +8

In this paper, we investigate the anti-Ramsey (more precisely, anti-van der Waerden) properties of arithmetic progressions. For positive integers $n$ and $k$ , the expression $aw([n…