Research
Research Interests
Graph Theory, Number Theory, and Combinatorics
Papers
Dana Neidmann, Directed graphs from exact covering systems, Journal of Integer Sequences 25 (2022), 22.2.4.
Dana Neidmann, Exact covering system digraphs of degree two, preprint 2022 available upon request.
Dana Neidinger and Douglas. B. West, Ramsey numbers of interval 2-chromatic ordered graphs. Graphs and Combinatorics 35, 1065–1076
Jesse Geneson, Amber Holmes, Xujun Liu, Dana Neidinger, Yanitsa Pehova, and Isaac Wass, Ramsey numbers of ordered graphs under graph operations, preprint 2019 available at arxiv.org/abs/1902.00259.
What I'm currently thinking about:
Graphs on the integers
Given a set of number-theoretically defined rules, we can create directed graphs on the integers. What can be said about the structure of these graphs, and what does it have to say about non-standard digital representations?
Spring 2018 — present
Work under Bruce Reznick
What I've thought about in the past:
Ramsey numbers of ordered graphs under graph operations
Given certain operations on ordered graphs, how much can the Ramsey number of the ordered graph change? Can we find tight bounds for these operations? (available at arxiv.org/abs/1902.00259)
Summer — Fall 2018
Work at GRWC jointly with Jesse Geneson, Amber Holmes, Xujun Liu, Yani Pehova, and Isaac Wass
Exact Ramsey numbers of all ordered graphs on at most 4 vertices
We are finding exact Ramsey numbers for all 4-vertex graphs, and we give exact Ramsey numbers for several families of ordered graphs.
Summer 2018 — present
Work at GRWC jointly with Amber Holmes, Jesse Geneson, Bernard Lidicky, Xujun Liu, Yanitsa Pehova, and Isaac Wass
Graduate Research Workshop in Combinatorics (GRWC) 2018
Reconfigurable power domination
Power domination is an topic related to zero-forcing with industrial applications: how can we obeserve every power station in a network? What if that network can change?
Summer 2018, GRWC
Work at GRWC
Algebraic voting theory
Weighted ranked voting systems and their properties. (pdf)
Spring 2016, Carleton College
Work under Peri Shereen jointly with Jordan Cahn, John Eckert, and Margalo Mullaney
Ramsey numbers of interval 2-chromatic ordered graphs
Ramsey numbers, extremal numbers, and how they relate to interval chromatic number. More specifically finding Ramsey numbers of interval chromatic number 2 ordered graphs. (available at arxiv.org/abs/1805.05900)
Summer 2017
Work under Douglas B. West