Nathan Warnberg

activity

20182022

collaborators

Showing math.COShow all

7 papers · 1 filter

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

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…