Research

My research lies in graph coloring, extremal combinatorics, and applied graph theory. In particular, for the latter two areas, I look at applying different coloring techniques to variations of Turan problems and studying the polytopes associated with the coloring linear programs. 

Submitted Preprints and Publications

1. S. Borgwardt, N. Crawford, S. Kafer, J. Lee, A. Morrison: On Circuit Imbalance and 0/1 Circuits for Coloring and Spanning Forest Problems (Submitted 2025)

2. N. Crawford, V. Irsic-Chenowith: Cop Number of Partial Cubes (Submitted 2025)

3. N. Crawford, M. Sankar, C. Schildkraut, S. Spiro: Rainbow Trees in Hypercubes (Submitted 2025)

4. N. Crawford, E. Heath, O. Henderschedt, C. Schwieder, S. Zerbib: Odd Ramsey Numbers of Complete Multipartite Graphs and Hypergraphs (Submitted 2025)

5. N. Crawford, D. King, S. Spiro: Erdős-Sos Conjecture for the Hypercube (Submitted 2025)

6. N.Crawford, V. Irsic: K-Hyperopic Cops and Robbers (Submitted 2024)

7. S. Borgwardt, N. Crawford, D. Horton, A. Morrison, E. Speakman: Evacuation Planning on Time- Expanded Networks with Integrated Wildfire Information (Submitted 2024)

8. J. Anderson et al. (9 authors) The Forb-Flex Method for Odd Coloring and Proper Conflict-Free Coloring of Planar Graphs (Discrete Mathematics Volume 348, 2024)

9. M. Carr, E. Cho, N. Crawford, V. Irsic, L. Pai, R. Robinson: On the Interval Coloring Impropriety of Graphs (Ars Combinatroia Volume 164, 2024)

10. N. Crawford, S. Jahanbekam: 3-colorability of Graphs with Minimum Degree at Least 6 (2022)

11. N. Crawford, S. Jahanbekam, K. Potika: Improved algorithm to determine 3-colorability of graphs with minimum degree at least 7 (Discrete Applied Mathematics Volume 298, 2020)