Research

Publications and Preprints:

• The forb-flex method for odd coloring and proper conflict-free coloring of planar graphs (with James Anderson, Herman Chau, Eun-Kyung Cho, Nicholas Crawford, Stephen G. Hartke, Owen Henderschedt, Hyemin Kown, and Zhiyuan Zhang), submitted. 

• Asymmetric Ramsey properties of randomly perturbed graphs (with Daniel McGinnis), submitted. 

• New bounds on f(n,5,8) (with Enrique Gomez-Leos, Alex Parker, Coy Schwieder, and Shira Zerbib), submitted.

• Edge-coloring a graph G so that every copy of a graph H has an odd color class (with Patrick Bennett and Shira Zerbib), submitted.

• The maximum number of odd cycles in a planar graph (with Ryan Martin and Chris Wells), submitted.

• Embedded graph 3-coloring and flows (with Caroline Bang, Zdeněk Dvořák, and Bernard Lidický), submitted.

• Online Ramsey numbers of ordered paths and cycles (with Felix Clemen and Mikhail Lavrov), submitted.

• Lower bounds on the  Erdős-Gyárfás problem via color energy graphs (with József Balogh, Sean English, and Robert Krueger), Journal of Graph Theory, (2023) 1-23.

• New upper bounds for the Erdős-Gyárfás problem on generalized Ramsey numbers (with Alex Cameron), Combinatorics, Probability, and Computing, 32 (2023) 349-362.

• A strengthening of the Erdős-Szekeres theorem (with József Balogh, Felix Clemen, and Mikhail Lavrov), European Journal of Combinatorics, 101 (2022), 103456. 

• Generalized rainbow Turán numbers of odd cycles (with József Balogh, Michelle Delcourt, and Lina Li), Discrete Mathematics, 345(2) (2022), 112663.

• Hypergraph models of biological networks to identify genes critical to pathogenic viral response (with S. Feng, B. Jefferson, C. Joslyn, H. Kvinge, J. McDermott, . . . , E. Purvine), BMC Bioinformatics, 22 (2021) 1-21.

• Ordered size Ramsey number of paths (with József Balogh, Felix Clemen, and Mikhail Lavrov), Discrete Applied Mathematics, 276 (2020) 13-18.

• A (5,5)-coloring of the complete graph with few colors (with Alex Cameron), Combinatorics, Probability and Computing, 27(6) (2018) 892-912.

• Economical extremal hypergraphs for the Erdős-Selfridge Theorem (with Eric Sundberg), Discrete Mathematics, 339(9) (2016) 2329-2344.

Graduate Research Mentoring:

I led three early-graduate research projects as part of the NSF Research Training Group on Combinatorics, Computation, and Applications at Iowa State University.

• Spring 2024: Rainbow Saturation

• Spring 2023: Generalized Ramsey Numbers

• Fall 2021: Random Perturbation of Graphs

I am leading a graduate research project started as part of the Graduate Research Workshop in Combinatorics, an annual two-week workshop for advanced graduate students to work in small collaborative groups with faculty and postdocs on problems in combinatorics.

• July 2023: Online Ordered Ramsey Theory

Undergraduate Research Mentoring:

I served as a graduate student mentor for three undergraduate research projects through the Illinois Geometry Lab at the University of Illinois Urbana-Champaign.

• Fall 2020: Mathematics of Change-ringing and the Altgeld Chimes (led by Jeremy Tyson)

• Summer 2020: Saturation Problems for Paths in Hypergraphs (led by Sean English)

• Spring 2020: Majestic Colorings of Graphs (led by Sean English)