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 13 successful undergraduate research projects. While on sabbatical during the 2019-2020 academic year, I focused on enhancing my ability to supervise undergraduate mathematical research projects.
In January 2024, I along with Haley Broadus and Gabriel Sharbel (both South Alabama undergraduate students), established the Coloring Research Group of South Alabama (CRGSA). The group aims to cultivate a vibrant research community, dedicated to producing original contributions in the field of graph coloring and broadening participation in math research. The CRGSA is always interested in recruiting new high school, undergraduate, and graduate collaborators. 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 13 successful undergraduate research projects. While on sabbatical during the 2019-2020 academic year, I focused on enhancing my ability to supervise undergraduate mathematical research projects.
In January 2024, I along with Haley Broadus and Gabriel Sharbel (both South Alabama undergraduate students), established the Coloring Research Group of South Alabama (CRGSA). The group aims to cultivate a vibrant research community, dedicated to producing original contributions in the field of graph coloring and broadening participation in math research. The CRGSA is always interested in recruiting new high school, undergraduate, and graduate collaborators. If you have some familiarity with graph theory and are interested in collaborating on research, do not hesitate to contact me!
Completed CRGSA Student Research Projects
- An Ohba-like Result for Flexible List Coloring, submitted
- Maximizing satisfied vertex requests in list coloring, Congressus Numerantium, 237 (2026) 121-141.
- Enumeratively chromatic-choosable theta graphs, Enumerative Combinatorics and Applications, 6(3) (2026) S2R23.
- On polynomial representations of dual DP color functions, Discussiones Mathematicae Graph Theory, 46(1) (2026) 67-90.
Completed CLC Student Research Projects
Presentations
- On the Ohba number and generalized Ohba numbers of complete bipartite graphs, Graphs and Combinatorics, 42(3) (2026) 44.
- On polynomial representations of the DP color function: theta graphs and their generalizations, Journal of Combinatorics, 15(4) (2024) 451-468.
- The DP color function of clique-gluings of graphs, Enumerative Combinatorics and Applications, 4(2) (2024) S2R11.
- On the list color function threshold, Journal of Graph Theory, 105(3) (2024) 386-397.
- 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(5) (2022) 163.
- The DP color function of joins and vertex-gluings of graphs, Discrete Mathematics, 345(11) (2022) 113093.
- Proportional 2-choosability with a bounded palette, Graphs and Combinatorics, 38(1) (2022) 23.
- On list equitable total colorings of the generalized theta graph, Discussiones Mathematicae Graph Theory, 41(4) (2021) 1215-1233.
- A note on the equitable choosability of complete bipartite graphs, Discussiones Mathematicae Graph Theory, 41(4) (2021) 1091-1101.
- Answers to two questions on the DP color function, The Electronic Journal of Combinatorics, 28(2) (2021) P2.24.
- Proportional choosability of complete bipartite graphs, Graphs and Combinatorics, 37(1) (2021) 381-392.
Presentations
- Enumerative Chromatic Choosability of Multipartite Graphs, poster presented by Morgan Taylor at the Joint Mathematics Meetings in Washington D.C. on January 6, 2026.
- Introducing... The Coloring Research Group of South Alabama, talk that summarizes two research projects completed by the Coloring Research Group of South Alabama that was delivered by Jeff Mudrock at the South Alabama Math & Stats Colloquium on January 30, 2025.
- Maximizing Satisfied Requests in List Coloring, poster presented by Gabriel Sharbel at the South Alabama Undergraduate Research Symposium on October 23, 2024.
- 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.
