Research
Research Statement (2022)
My research interests lie mostly in combinatorics and graph theory. Broadly speaking, I am interested in applying techniques from enumerative combinatorics, algebraic combinatorics, probabilistic combinatorics, and extremal combinatorics to solve problems in graph theory. I am also interested in applications of my research to computer science. As an undergraduate, I studied graph labelings as a means of attacking the problem of decomposing classes of complete graphs, circulant graphs, and multigraphs, cyclically. Currently, I am studying graph coloring problems using extremal, algebraic, and probabilistic techniques.
Below is a list of some of my publications and preprints:
My research interests lie mostly in combinatorics and graph theory. Broadly speaking, I am interested in applying techniques from enumerative combinatorics, algebraic combinatorics, probabilistic combinatorics, and extremal combinatorics to solve problems in graph theory. I am also interested in applications of my research to computer science. As an undergraduate, I studied graph labelings as a means of attacking the problem of decomposing classes of complete graphs, circulant graphs, and multigraphs, cyclically. Currently, I am studying graph coloring problems using extremal, algebraic, and probabilistic techniques.
Below is a list of some of my publications and preprints:
- “A polynomial method for counting colorings of S-labeled graphs”, with S. Dahlberg and H. Kaul, submitted [arXiv]
- “DP-coloring of graphs from random covers”, with A. Bernshteyn, D. Dominik, and H. Kaul, submitted [arXiv]
- “An algebraic approach for counting DP-3-colorings of sparse graphs”, with S. Dahlberg and H. Kaul, submitted. [arXiv]
- "Flexible list colorings: Maximizing the number of requests satisfied", with H. Kaul, R. Mathew, and M. Pelsmajer, submitted. [arXiv]
- “The DP color function of clique-gluings of graphs”, with H. Kaul, M. Maxfield, and S. Thomason, submitted. [arXiv]
- “On polynomial representations of the DP color function: theta graphs and their generalizations”, with C. Halberg, H. Kaul, A. Liu, P. Shin, and S. Thomason, submitted. [arXiv]
- "A note on fractional DP-coloring of graphs", with H. Kaul and D. Dominik, submitted. [arXiv]
- “On the list color function threshold”, with H. Kaul, A. Kumar, P. Rewers, P. Shin, and K. To, to appear in Journal of Graph Theory. [arXiv]
- “Bounding the list color function threshold from above”, with H. Kaul, A. Kumar, A. Liu, P. Rewers, P. Shin, M. S. Tanahara, and K. To, Involve, 16(5) (2023), 849-882. [arXiv]
- “A short proof that the list packing number of any graph is well defined”, Discrete Mathematics, 346(11) (2023) 113185. [arXiv]
- “DP-coloring Cartesian products of graphs”, with H. Kaul, G. Sharma, and Q. Stratton, Journal of Graph Theory, 103(2) (2023) 285-306. [arXiv]
- “Non-chromatic-adherence of the DP color function via generalized theta graphs”, with M. V. Bui, H. Kaul, M. Maxfield, P. Shin, and S. Thomason, Graphs and Combinatorics, 39 (2023) 42. [arXiv]
- “On the equitable choosability of the disjoint union of stars”, with H. Kaul and T. Wagstrom, Graphs and Combinatorics, 38 (2022) no. 5, 163. [arXiv]
- “The DP color function of joins and vertex-gluings of graphs”, with J. Becker, J. Hewitt, H. Kaul, M. Maxfield, D. Spivey, S. Thomason, and T. Wagstrom, Discrete Mathematics, 345 (2022) 113093. [arXiv]
- “A deletion-contraction relation for the DP color function”, Graphs and Combinatorics, 38 (2022) 115. [arXiv]
- “On proportional 2-choosability with a bounded palette”, with R. Piechota, P. Shin, and T. Wagstrom, Graphs and Combinatorics, 38 (2022) 23. [arXiv]
- "On equitable list arborictiy of graphs", with H. Kaul and M. Pelsmajer, Australasian Journal of Combinatorics, 80 (2021) 419-441. [arXiv]
- “Criticality, the list color function, and list coloring the Cartesian product of graphs”, with H. Kaul, Journal of Combinatorics, 12 (2021) 479-514. [arXiv]
- "On list equitable total colorings of the generalized theta graph", with M. Marsh and T. Wagstrom, Discussiones Mathematicae Graph Theory, 41 (2021) 1215-1233. [arXiv]
- “A note on the equitable choosability of complete bipartite graphs”, with M. Chase, I. Kadera, E. Thornburgh, and T. Wagstrom, Discussiones Mathematicae Graph Theory, 41 (2021) 1091-1101. [arXiv]
- “Answers to two questions on the DP color function”, with S. Thomason, The Electronic Journal of Combinatorics, 28 (2021) P2.24. [arXiv]
- "Partial DP-coloring", with H. Kaul and M. Pelsmajer, Discrete Mathematics, 344 (2021) 112306. [arXiv]
- “On the chromatic polynomial and counting DP-colorings”, with H. Kaul, Advances in Applied Mathematics, 123 (2021) 102131. [arXiv]
- “Proportional choosability of complete bipartite graphs”, with J. Hewitt, P. Shin, and C. Smith, Graphs and Combinatorics, 37 (2021) 381-392. [arXiv]
- “Combinatorial nullstellensatz and DP-coloring of graphs”, with H. Kaul, Discrete Mathematics, 343 (2020) 112115. [arXiv]
- “A simple characterization of proportionally 2-choosable graphs”, with H. Kaul, M. Pelsmajer, and B. Reiniger, Graphs and Combinatorics 36 (2020) 679-687. [arXiv]
- “List coloring a Cartesian product with a complete bipartite factor”, with H. Kaul, Graphs and Combinatorics 35 (2019) 1571-1583. [arXiv]
- “Proportional choosability: a new list analogue of equitable coloring”, with H. Kaul, M. Pelsmajer, and B. Reiniger, Discrete Mathematics, 342 (2019) 2371-2383. [arXiv]
- “On the Alon-Tarsi number and chromatic-choosability of Cartesian products of graphs”, with H. Kaul, The Electronic Journal of Combinatorics, 26 (2019) P1.3. [arXiv]
- “Total equitable list coloring”, with H. Kaul and M. Pelsmajer, Graphs and Combinatorics, 34 (2018) 1637-1649. [arXiv]
- “A note on the DP-chromatic number of complete bipartite graphs”, Discrete Mathematics, 341 (2018) 3148-3151. [arXiv]
- “On lambda-fold Rosa-type labelings of bipartite multigraphs”, with R. C. Bunge, S. I. El-Zanati, C. Vanden Eynden, W. Wannasit, Electronic Notes in Discrete Mathematics, 60 (2017) 11-23. [doi]
- “On labeling 2-regular graphs where the number of odd components is at most 2”, with R. C. Bunge, S. I. El-Zanati, M. Hirsch, D. Klope, K. Sebesta, and B. Shafer, Utilitas Mathematica, 91 (2013) 261-285. [REU]
- “An observation on generating functions with an application to a sum of secant powers”, Involve, 4 (2012) 117-125. [journal]
- “On cyclic decompositions of circulant graphs into almost-bipartite graphs”, with S. I. El-Zanati and K. King, Australasian Journal of Combinatorics, 49 (2011) 61-76. [REU]