Research

My research interests lie in combinatorics, graph theory and applications. 

I am running an REU program at Fairfield this summer, 2024. I am also one of the mentors for the Polymath Jr REU online summer research program, for more information about the application process visit here. 

I am the organizer of the Fairfield Math Research Symposium. Students interested in giving a talk, please fill out this form (or email me). 

• On the Correspondence Between Integer Sequences and Vacillating Tableaux, with P. E. Harris, A. Pun, C. Yan, C. Zhao. Submitted. arXiv:2405.07093 

• Bounds for Rainbow-uncommon Graphs, with B. Bates, N. Chiem, G. Elvin, R. Fines, M. Lie, H. Mikulas, I. Reiter, K. Zhou. Submitted. arXiv:2403.04055 

• Anti-van der Waerden Numbers of Graph Products with Trees, with  J. Miller, E. Sprangel, S. Walker, N. Warnberg. Submitted. arXiv:2310.20462

• On the existence of $(r,g,\chi)$-cages, with G. Araujo-Pardo and L. Lesniak. Submitted. arXiv:2304.03825

• Combinatorial Identities of Vacillating Tableaux, with P.E. Harris, A. Pun, C. Yan, and C.C. Zhao. To appear in Integers. arXiv:2308.14183

• On the limiting vacillating tableaux for integer sequences, with P. E. Harris, A. Pun, C. Yan, and C. Zhao. To appear in Journal of Combinatorics.

• Rainbow Solutions to the Sidon Equation in Cyclic Groups, with J. Kritschgau. Discrete Mathematics, 347:9 (2024).

• Triangle-degree and triangle-distinct graph, with B. Bjorkman, H.C. Smith, S. Jahanbekam, B. Kay, L. Keough, B. McKain, K. Moss, D. Rorabaugh, S. Shan. Discrete Mathematics, 347:1 (2024)

• Anti-van der Waerden numbers on Graphs, with A. Schulte, E. Sprangel, S. Walker, N. Warnberg, M. Young. Journal of Graphs and Combinatorics. 38: 124 (2022)

• Finding Long Cycles in Balanced Tripartite Graphs: A First Step (book chapter), with G. Araujo-Pardo, J. Faudree, K. Hogenson, R. Kirsch, L. Lesniak, J. McDonald. In Daniela Ferrero et al. (eds) Research Trends in Graph Theory, Association for Women in Mathematics Series (peer-reviewed). Springer Nature, Cham, Switzerland (2021).

• List-antimagic Labeling of Vertex-Weighted Graphs, with A. Brandt, S. Jahanbekam, V. Larsen, D. Rorabaugh. Discrete Mathematics & Theoretical Computer Science. 23:3 (2021).

• On the Edit Distance of Powers of Cycles, with R. Martin, C. Peck. Discrete Mathematics. 342, 2804--2817 (2019).

• A forest building process on simple graphs, with S. Butler, J. Cummings, K. Heysse, P. Horn, R. Luo, B. Moran. Discrete Mathematics. 341, 497--507 (2018).

• Proof of a conjecture of Graham and Lovász concerning unimodality of coefficients of the distance characteristic polynomial of a tree, with G. Aalipour, A. Abiad, L. Hogben, F. Kenter, J. Lin, M. Tait. Electronic Journal of Linear Algebra. 34, 373--380 (2018).

• Anti-van der Waerden numbers of 3-term arithmetic progressions, with A. Schulte, M. Young. Electronic Journal of Combinatorics. 24(2): P2.39 (2017).

• (4, 2)-choosability of planar graphs with forbidden substructures, joint work with C. Cox, M. Dairyko, K. Hogenson, M. Kumbhat, B. Lidický, K. Messerschmidt, K. Moss, K. Nowak, K. Palmowski, D. Stolee. Graphs and Combinatorics. I33, 751--787 (2017).

• On the distance spectra of graphs, with G. Aalipour, A. Abiad, J. Cummings, J. De Silva, W. Gao, K. Heysse, L. Hogben, F. Kenter, J. Lin, M. Tait. Linear Algebra and its Applications. 497: 66-87 (2016).

• Mathematical Model of Micro-Asperity Explosion in Vacuum Circuit Breakers, with S. N. Kharin. Proceedings of the 4th International Conference on Electronics, Computer, and Computation (ICECCO), pp. 194-200, Almaty, Kazakhstan (2007). [pdf]

• Метод решения обратной задачи Веригина о водонефтяном контакте в условиях упругого режима, Ж.Бериккызы, С. Н. Харин. Математический журнал, Том 8, № 2 (28), с. 38 – 43,  Алматы (2008).  (In Russian)