Profile for Nathan Warnberg

Research and publishing

• Z. Berikkyzy, J. Miller and N. Warnberg. Full Classification of anti-van der Waerden numbers of graph products of forests. Submitted, Preprint: https://arxiv.org/abs/2504.00288
• H. Schuerger, N. Warnberg and M. Young. Zero Forcing and Vertex Independence Number on Cubic and Subcubic Graphs. Submitted, Preprint:  https://arxiv.org/abs/2410.21724
• Z. Berikkyzy, J. Miller, E. Sprangel, S. Walker and N. Warnberg. Anti-van der Waerden Number of Graph Products with Trees. Submitted, Preprint:https://arxiv.org/abs/2310.20462.
• J. Miller and N. Warnberg. Anti-van der Waerden Number of Graph Products of Cycles. Australas. J. Combin. 87(1) (2023), 24–40. https://ajc.maths.uq.edu.au/?page=get_volumes&volume=87
• K. Fallon, E. Manhart, J. Miller, H. Rehm, N. Warnberg and L. Zinnel, Rainbow Numbers of [m] × [n] for x1 + x2 = x3. Integers 23 (2023), A47. http://math.colgate.edu/~integers/vol23.html.
• Helping Students Fail Productively. MAA Math Values Blog, January 5, 2023.
  https://www.mathvalues.org/masterblog/helping-students-fail-productively
• Anti-van der Waerden Numbers on Graphs. (with Z. Berikkyzy t al.). Graphs and Combinatorics, 38(124), (2022). https://doi.org/10.1007/s00373-022-02516-9
• On leaky forcing and resilience (with J. Alameda, J. Kritshgau and M. Young)   Discrete Applied Math, 306, 32--45 (2022). https://doi.org/10.1016/j.dam.2021.09.005
• Rainbow Numbers of Z_n for a_1x_1+a_2x_2 + a_3x_3 = b (with K. Ansaldi et al.)    INTEGERS, 20, A51 (2020). http://math.colgate.edu/~integers/vol20.html
• Anti-Schur numbers for sum_{i=1}^{k-1} x_i=x_k in [n], (with K. Fallon et al.), Australasian Journal of Combinatorics, 77(1), 1--8 (2020). https://ajc.maths.uq.edu.au/pdf/77/ajc_v77_p001.pdf
• Properties of a $q$-analgue of zero forcing, \emph{Graphs and Combinatorics (with S. Butler et al.),  36, 1401--1419 (2020). https://doi.org/10.1007/s00373-020-02208-2
• Directionality of the Equals Sign (with T. Das and W. George), PRIMUS, 2019. https://www.tandfonline.com/doi/full/10.1080/10511970.2019.1608486

• Anti-van der Waerden Numbers on Graph Products (with H. Rehm and A. Schulte), Australasian Journal of Combinatorics, 73(3), 2019. https://ajc.maths.uq.edu.au/pdf/73/ajc_v73_p486.pdf

• Zero forcing propagation time on oriented graphs (with A. Berliner et al.), Discrete Applied Math, 224, 2017. https://doi.org/10.1016/j.dam.2017.02.017

• Rainbow arithmetic progression (with S. Butler et al.), Journal of Combinatorics, 7(4), 2016. https://dx.doi.org/10.4310/JOC.2016.v7.n4.a3

• Positive semidefinite propagation time. Discrete Applied Math, 198, 2016. https://doi.org/10.1016/j.dam.2015.04.008

• Path cover number, maximum nullity, and zero forcing number of oriented graphs and other simple digraphs (with A. Berliner et al.). Involve, a Journal of Mathematics, 8(1), 2015. http://dx.doi.org/10.2140/involve.2015.8.147
  
  
• Computing positive semidefinite minimum rank for small graphs (with S. Osborne). Involve, a Journal of Mathematics, 7(5), 2014. http://dx.doi.org/10.2140/involve.2014.7.595
  
  
• Positive semidefinite zero forcing (with J. Ekstrand et al.). Linear Algebra and Applications, 439(7), 2013. https://doi.org/10.1016/j.laa.2013.05.020

Papers Under Review

• K. Fallon, E. Manhart, J. Miller, H. Rehm, N. Warnberg and L. Zinnel, Rainbow numbers of [m]\times [n] for x_1 + x_2 = x_3. Preprint: https://arxiv.org/abs/2301.10349
• J. Miller and N. Warnberg.  Anti-van der Waerden Number of Graph Products of Cycles. Preprint: https://arxiv.org/abs/2205.11621