Research
Research
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My adviser (Chris Rodger), me, my adviser's adviser (Tony Hilton)!
Auburn University, Spring 2019
Research Assistants
Hiroshi Nonaka, Fall 2023 - Present
Sarah Johnson, Fall 2022 - Spring 2023, Winter 2023 - Present
Ha Nguyen, Winter 2024 - Spring 2024
Yoichi Watanabe, Summer 2023
Rio Primandaru, Summer 2022, Fall 2022
Rodrigo Morais, Fall 2021 - Spring 2022
Capstone Students
Parik Chalise '22
PhD student in Applied Mathematics at Johns Hopkins University
Soka University Excellence in Academics Award
Biplab Karki '22
Robotics Support Engineer at Amazon London
Rodrigo Morais '22
Full Stack Data Scientist at Star Parks
My primary area of concentration is discrete mathematics, specifically the fields of graph theory and design theory. To date, my research has been primarily focused on problems involving graph decompositions and graph embeddings, which can often be interpreted both from a graph theory perspective and from a design theory one. My research has involved tools from both areas, as well as computer programming to answer such questions.
Specific questions I have worked on have been related to rainbow spanning trees (RSTs) in graphs: the Brualdi-Hollingsworth Conjecture, maximizing and minimizing the number of RSTs in an edge-colored graph, finding certain RSTs in graphs, and determining which RSTs can exist in a given graph, but I have also investigated problems dealing with block decompositions of almost complete graphs and a graph optimization, called throttling, for the game of cops and robbers on graphs.
With my three 2022 senior capstone students at graduation! (left to right: Parik Chalise, Rodrigo Morais, and Biplab Karki)
Publications
Sonwabile Mafunda, Jonathan L. Merzel, K. E. Perry, Anna Varvak. Paint cost spectrum of perfect k-ary trees. (Submitted.)
Debra Boutin, Sally Cockburn, Lauren Keough, Sarah Loeb, K. E. Perry, Puck Rombach. Determining Number and Cost of Generalized Mycielskian Graphs. Discussiones Mathematicae Graph Theory Vol 44 No. 1 (2024), 127--150.
Calum Buchanan, Brandon Du Preez , K. E. Perry, and Puck Rombach. Toughness of recursively partitionable graphs. Theory and Applications of Graphs Vol. 10 Iss. 2, Article 4 (2023).
Matthew DeVilbiss, Bradley Fain, Amber Holmes, Paul Horn, Sonwabile Mafunda, K. E. Perry. An Extremal Problem on Rainbow Spanning Trees in Graphs. Australasian Journal of Combinatorics 86(1) (2023), 1--23.
Debra Boutin, Sally Cockburn, Lauren Keough, Sarah Loeb, K. E. Perry, Puck Rombach. Distinguishing Generalized Mycielskian Graphs. Australasian Journal of Combinatorics 83(2) (2022), 225--242.
Anthony Bonato, Jane Breen, Boris Brimkov, Josh Carlson, Sean English, Jesse Geneson, Leslie Hogben, K. E. Perry, Carolyn Reinhart. Optimizing the trade-off between number of cops and capture time in Cops and Robbers. Journal of Combinatorics 13:1 (2022).
Debra Boutin, Sally Cockburn, Lauren Keough, Sarah Loeb, K. E. Perry, Puck Rombach. Symmetry Parameters for Mycielskian Graphs. (2021) In: Ferrero D., Hogben L., Kingan S.R., Matthews G.L. (eds) Research Trends in Graph Theory and Applications. Association for Women in Mathematics Series, vol 25. Springer, Cham.
Joshua Carlson, Andrew Owens, K. E. Perry, Inne Singgih, Zi-Xia Song, Donglei Yang, Fangfang Zhang, Xiaohong Zhang. Antimagic orientations of graphs with large maximum degree. Discrete Mathematics 343:12 (2020).
Jane Breen, Boris Brimkov, Joshua Carlson, Leslie Hogben, K. E. Perry, Carolyn Reinhart. Throttling for the Game of Cops and Robbers on Graphs. Discrete Mathematics 341:9 (2018), 2418--2430.
Hung-Lin Fu, Yuan-Hsun Lo, K. E. Perry, C. A. Rodger. On the Number of Rainbow Spanning Trees in Edge-Colored Complete Graphs. Discrete Mathematics 341:8 (2018), 2343--2352.
Supervised Publications
The following book was written, illustrated, and independently published as a final project for my Winter Learning Clusters: Folk and Fairy Tales in a Global Context.
C. Cozort, F. del Cielo, P. Duong, G. Guion, M. Hashimoto, B. Martel, S. Middleswart, R. Ottman, A. Saito, A. Stallworth, I. Stoliarova, authors. K.E. Perry, editor. Perry Tales Anthology. Independently Published, 2021.
H. Adachi, A. Agrawal, P. Chinpattanakul, N. Guzman, M. Lam, S. Meyers, T. Misra, C. Pierce, T. Suetake, R. Sugihara, T. Wang, J. Williams, authors. K. E. Perry, editor. Perry's Choice: 12 Fables. Independently Published, 2022.
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