- combinatorics
- mathematics
- theoretical computer science
Education summary
- PhD, Simon Fraser
- MSc, Victoria
- BSc, Simon Fraser
Research summary
My research is in the area of matroid structure theory. Mostly, I study various sorts of quasi-graphic matroids: imagine a set of points in space, with various collections of points contained in lines, planes, and hyperplanes, and (somehow) the geometry of these points describes the structure of some network.
Families of matroids are often best understood by considering the unavoidable substructures all members of the family must or must not contain. For example, Kuratowski’s theorem says that a graph may be drawn in the plane if and only if it does not contain the complete graph on five vertices or the complete bipartite graph with each part of size three. A classic theorem of Tutte (with whom I am posing in the photo) describes a set of five matroids that no graphic matroid can contain, and, like Kuratowski’s theorem, shows that these five are the only obstructions for a matroid to being graphic. We thus completely understand which structures are fundamentally graphic, and which are not, and why. My research focuses on the analogous question, “Which structures are quasi-graphic?”
Publications and other research outputs
- Matt DeVos, Daryl Funk, Luis Goddyn, Gordon Royle. There are only a finite number of excluded minors for the class of bicircular matroids. Submitted (November 2022). https://arxiv.org/abs/2102.02929
- Daryl Funk & Daniel Slilaty, Matrix representations of frame and lifted-graphic matroids correspond to gain functions, Journal of Combinatorial Theory Series B. (July 2022). https://arxiv.org/abs/1609.05574
- Daryl Funk, Dillon Mayhew, & Mike Newman, Tree automata and pigeonhole classes of matroids - I, Algorithmica 84:1795–1834 (January 2022). https://arxiv.org/abs/1910.04360
- Matt DeVos, Matthew Drescher, Daryl Funk, Sebasti´an Gonz´alez Hermosillo de la Maza, Krystal Guo, Tony Huynh, Bojan Mohar, Amanda Montejano, Short rainbow cycles in graphs and matroids, Journal of Graph Theory (June 2020). https://arxiv.org/abs/1806.00825
- Jason Bell, Daryl Funk, Byoung Du Kim, Dillon Mayhew. Effective versions of two theorems of Rado, Quarterly Journal of Mathematics, (June 2020). https://arxiv.org/abs/1802.10262Daryl
- Funk, Dillon Mayhew, Mike Newman, Defining bicircular matroids in monadic logic. Submitted (May 2020) https://arxiv.org/abs/2005.04526
- Nathan Bowler, Daryl Funk, & Daniel Slilaty, Describing Quasi-Graphic Matroids, European Journal of Combinatorics Volume 85 (March 2020). https://arxiv.org/abs/1808.00489
- Daryl Funk, Dillon Mayhew, & Mike Newman, Tree automata and pigeonhole classes of matroids - II, Submitted (2019). https://arxiv.org/abs/1910.04361
- Daryl Funk & Dillon Mayhew. On excluded minors for classes of graphical matroids, Discrete Mathematics, Volume 341 (June 2018), 1509-1522. https://arxiv.org/abs/1706.06265
- Daryl Funk, Dillon Mayhew, & Steven D. Noble. How many delta-matroids are there? European Journal of Combinatorics, Volume 69 (March 2018), 149-158. https://arxiv.org/abs/1609.08244
- Matt DeVos & Daryl Funk, Almost balanced biased graph representations of frame matroids, Advances in Applied Mathematics, Volume 96 (2018), 139-175. http://arxiv.org/abs/1606.07370
- Matt DeVos, Daryl Funk, & Irene Pivotto, On excluded minors of connectivity 2 for the class of frame matroids, European Journal of Combinatorics, Volume 61 (2017), 167-196. http://arxiv.org/abs/1502.06896
- Rong Chen, Matt DeVos, Daryl Funk, & Irene Pivotto, Graphical Representations of Graphic Frame Matroids, Graphs and Combinatorics, Volume 31 (2015), 2075-2086. http://arxiv.org/abs/1403.7733
- Matt DeVos, Daryl Funk, & Irene Pivotto, When does a biased graph come from a group labelling? Advances in Applied Mathematics, Volume 61 (2014), 1-18. https://arxiv.org/abs/1403.7667
- Richard C. Brewster & Daryl Funk, On the Hamiltonicity of line graphs of locally finite, 6-edge-connected graphs, Journal of Graph Theory, Volume 71 (2012), 182-191. https://onlinelibrary.wiley.com/doi/pdf/10.1002/jgt.20641
Courses taught
Ongoing projects
- Personal webpage: https://sites.google.com/site/darylfunk/