Student Research
I enjoy collaborating on mathematical research problems with both undergraduate and graduate students. During my time at the College of Lake County, I created an undergraduate research course which led to several successful projects. While on sabbatical during the 2019-2020 academic year, I focused on enhancing my ability to supervise undergraduate mathematical research projects. If you have some familiarity with graph theory and are interested in collaborating on research, do not hesitate to contact me!
I enjoy collaborating on mathematical research problems with both undergraduate and graduate students. During my time at the College of Lake County, I created an undergraduate research course which led to several successful projects. While on sabbatical during the 2019-2020 academic year, I focused on enhancing my ability to supervise undergraduate mathematical research projects. If you have some familiarity with graph theory and are interested in collaborating on research, do not hesitate to contact me!
Completed Student Research Projects
Presentations
- The DP color function of clique-gluings of graphs, submitted.
- On polynomial representations of the DP color function: theta graphs and their generalizations, submitted.
- On the list color function threshold, accepted in Journal of Graph Theory.
- Bounding the list color function threshold from above, Involve, 16(5) (2023), 849-882.
- Non-chromatic-adherence of the DP color function via generalized theta graphs, Graphs and Combinatorics, 39 (2023) 42.
- On the equitable choosability of the disjoint union of stars, Graphs and Combinatorics, 38 (2022) no. 5, 163.
- The DP color function of joins and vertex-gluings of graphs, Discrete Mathematics, 345 (2022) 113093.
- Proportional 2-choosability with a bounded palette, Graphs and Combinatorics, 38 (2022) 23.
- On list equitable total colorings of the generalized theta graph, Discussiones Mathematicae Graph Theory, 41 (2021) 1215-1233.
- A note on the equitable choosability of complete bipartite graphs, Discussiones Mathematicae Graph Theory, 41 (2021) 1091-1101.
- Answers to two questions on the DP color function, The Electronic Journal of Combinatorics, 28 (2021) P2.24.
- Proportional choosability of complete bipartite graphs, Graphs and Combinatorics, 37 (2021) 381-392.
Presentations
- On chromatic polynomials, list color functions, and DP color functions, talk which summarizes many undergraduate research projects that was delivered by Jeff Mudrock at the AMS Western Sectional Meeting on May 15, 2022.
- Equitable Choosability of the Disjoint Union of Stars, talk delivered by Tim Wagstrom at the Illinois Institute of Technology Discrete Applied Math Seminar on November 6, 2020.
- DP-coloring the Cartesian product of graphs, poster presented by Gunjan Sharma and Quinn Stratton at the Illinois Institute of Technology's Menger Day Poster Session on March 6, 2020.
- On proportional 2-choosability of graphs with a bounded palette, talk delivered by Paul Shin at the Illinois Institute of Technology Discrete Applied Math Seminar on October 14, 2019.
- Proportional 2-choosability of graphs with a restricted palette, poster presented by Paul Shin at the 2019 SPARK Symposium on October 3, 2019 and at the University of Illinois at Chicago Undergraduate Mathematics Symposium on November 2, 2019.
- The equitable choosability of complete bipartite graphs, poster presented by Tim Wagstrom at the Illinois Institute of Technology's Menger Day Poster Session on April 1, 2019 and at the University of Illinois at Chicago Undergraduate Mathematics Symposium on November 2, 2019.