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