Publications & Preprints
Trail Trap: A variant of Partizan Edge Geography with MacKenzie Carr, Alexander Clifton, Stephen G. Hartke, Vesna Iršič Chenoweth, Nicholas Sieger, and Rebecca Whitman; Discrete Applied Mathematics, 379:79-95, 2026.
A lower bound on the saturation number and a strengthening for triangle-free graphs with Puck Rombach; The Electronic Journal of Combinatorics, 32(3), #P3.14, 2025.
Vertex addition to a ball graph with application to reliability and area coverage in autonomous swarms
, CB, Puck Rombach, James Bagrow, and Hamid R. Ossareh; arXiv.2506.19197, 2025.
(Python implementation and code for the simulations is available at github.com/calum-buchanan/UDG-Neighborhoods-Reliability-AreaCoverage.)
On odd covers of cliques and disjoint unions with Alexander Clifton, Eric Culver, Péter Frankl, Jiaxi Nie, Kenta Ozeki, Puck Rombach, and Mei Yin; arXiv:2408.08598, 2024.
Tropical Geometry of Rado Matroids with Rick Danner; Discrete Mathematics Letters, 14:27-30, 2024.
Node Placement to Maximize Reliability of a Communication Network with Application to Satellite Swarms, CB, James Bagrow, Puck Rombach, and Hamid Ossareh; in 2023 IEEE International Conference on Systems, Man, and Cybernetics (SMC).
Toughness of recursively partitionable graphs with Brandon Du Preez, K. E. Perry, and Puck Rombach; Theory and Applications of Graphs, 10(2), Article 4, 2023.
Path odd-covers of graphs with Steffen Borgwardt, Eric Culver, Bryce Frederickson, Puck Rombach, and Youngho Yoo; arXiv:2306.06487, 2023.
Odd covers of graphs with Alexander Clifton, Eric Culver, Jiaxi Nie, Jason O'Neill, Puck Rombach, and Mei Yin; Journal of Graph Theory, 104(2):420-439, 2023.
On the last new vertex visited by a random walk in a directed graph with Paul Horn and Puck Rombach; Discrete Mathematics Letters, 11:96-98, 2023.
Subgraph complementation and minimum rank with Christopher Purcell and Puck Rombach; The Electronic Journal of Combinatorics, 29(1), #P1.38, 2022.
PhD Dissertation
Odd covers and graph saturation, University of Vermont, 2025.
Talks & Posters
List
of talks I've given
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Upcoming (Oct 10): a talk on saturation numbers at the DU Analysis & Dynamics Seminar
Slides
on saturation, semisaturation, and rainbow saturation numbers of double stars, for the 2025 AMS Spring Eastern Sectional Meeting
Slides
on the last new vertex visited by a random walk in a directed graph, for the 2023 Southern Africa Mathematical Sciences Association Annual Conference
Slides
on subgraph complementation and minimum rank, and a poster for the 2021 NE Combinatorics Network KLATCH
Poster
on odd covers of graphs for the 2022 Discrete Math Days
Workshops
Emléktábla
15th Emléktábla Workshop in Vác, Hungary, July 2024. I participated in the Extremal combinatorics group.
MASI
Masamu Advanced Study Institute and Workshops (virtual in 2020 and 2021, Pretoria, South Africa in 2023). I participated each time in the graph theory work group, meeting wonderful people and finding good problems to work on. The 2020 and 2021 workshops lead to the papers Toughness of recursively partitionable graphs and On the last new vertex visited by a random walk in a directed graph. A project from the 2023 workshop is underway.
GRWC
Graduate Research Workshop in Combinatorics (virtual in 2021, Denver, CO in 2022). I had the pleasure of working on a number of problems suggested by my fellow graduate students and of leading working groups on odd covers of graphs with bicliques in 2021 and on odd covers with paths and cycles in 2022.
SIAM MPI
Mathematical Problems in Industry Workshop, hosted by SIAM and the University of Vermont in 2024. I worked on an algorithm to match mentors with mentees for the Grad Leveraging Engaged Alumni Program at University of Delaware.
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Technical report: One Algorithm to Rule Them All with N. Brown, N. Chicoine, B. Emerick, A. Emmanuel, C. Hammond, K. Oluwasegun, O. Pomerenk, L. Schneegans, and H. Taboe. Mathematics in Industry Reports (submitted April 2025).
