My resarch interests include dicrete geometry, combinatorics, and topological methods therein. More recently, I have become interested in the interactions between algebra and combinatorics.
Below is the list of papers I have (co)authored in reverse chronological order that they appear on arXiv.
Multi-Graded Generic Initial Ideals, Regularity, and the Optimal Colorful Fractional Helly Theorem for d-Leray Complexes
D. McGinnis
16 pages.
arXiv
A Common Generalization to Strengthenings of Drisko’s Theorem for Intersections of Two Matroids
E. Berger and D. McGinnis
5 pages.
arXiv
A Topological Product Tverberg Theorem
A. F. Holmsen, G. McCourt, D. McGinnis, and S. Zerbib
Proceedings of the American Mathematical Society 154 (2026), pp. 1251–1260.
arXiv · DOI
A Necessary and Sufficient Condition for k-Transversals
D. McGinnis and N. Sadovek
Advances in Mathematics 490 (2026), 13 pages.
arXiv · DOI
Matroid Colorings of KKM Covers
D. McGinnis
16 pages.
arXiv
Using the KKM Theorem (survey paper)
D. McGinnis and S. Zerbib
Bolyai Society Mathematical Studies, 28 pages. Accepted.
arXiv
Ehrhart Positivity of Panhandle Matroids and the Ehrhart-Coefficient Upper Bound Conjecture for Paving Matroids
D. Deligeorgaki, D. McGinnis, and A. Vindas-Meléndez
SIAM Journal on Discrete Mathematics 40 (2026), pp. 576–601.
arXiv · DOI
Asymmetric Ramsey Properties of Randomly Perturbed Graphs
E. Heath and D. McGinnis
15 pages.
arXiv
The Existence and Structure of Universal Partial Cycles
D. Fillmore, B. Goeckner, R. Kirsch, K. Martin, and D. McGinnis
Designs, Codes and Cryptography 94 (2026), 37 pages.
arXiv · DOI
A Necessary and Sufficient Condition for (2d − 2)-Transversals in ℝ²ᵈ
D. McGinnis
Combinatorica 43 (2023), pp. 1103–1109.
arXiv · DOI
Ehrhart Positivity for a Certain Class of Panhandle Matroids
D. McGinnis
Journal of Combinatorics 16 (2025), pp. 43–64.
arXiv · DOI
Piercing Families of Convex Sets in the Plane That Avoid a Certain Subfamily with Lines
D. McGinnis
Computational Geometry: Theory and Applications 120 (2024).
arXiv · DOI
Lattice Points in Slices of Prisms
L. Ferroni and D. McGinnis
Canadian Journal of Mathematics 17 (2025), pp. 1013–1040.
arXiv · DOI
Ehrhart Theory of Paving and Panhandle Matroids
D. Hanely, L. J. Martin, D. McGinnis, D. Miyata, A. Vindas-Meléndez, and M. Yin
Advances in Geometry 23 (2023), pp. 501–526.
arXiv · DOI
A Sparse Colorful Polytopal KKM Theorem
D. McGinnis and S. Zerbib
Discrete & Computational Geometry 71 (2024), pp. 945–959.
arXiv · DOI
Improved Bounds on a Generalization of Tuza’s Conjecture
A. Basit, D. McGinnis, H. Simmons, M. Sinnwell, and S. Zerbib
Electronic Journal of Combinatorics 29 (2022), pp. 1–23.
arXiv · DOI
Accumulation Points of the Edit Distance Function
C. Cox, D. McGinnis, and R. R. Martin
Discrete Mathematics 345 (2022), pp. 112857–112874.
arXiv · DOI
Line Transversals in Families of Connected Sets in the Plane
D. McGinnis and S. Zerbib
SIAM Journal on Discrete Mathematics 36 (2022), pp. 2916–2919.
arXiv · DOI
A Family of Convex Sets in the Plane Satisfying the (4, 3)-Property Can Be Pierced by Nine Points
D. McGinnis
Discrete & Computational Geometry 68 (2022), pp. 860–880.
arXiv · DOI
A Method to Construct 1-Rotational Factorizations of Complete Graphs and Solutions to the Oberwolfach Problem
D. McGinnis and E. Poimenidou
Journal of Combinatorial Designs 27 (2019), pp. 106–117.
arXiv · DOI
Extremal Problems Related to the Cardinality Redundance of Graphs
D. McGinnis and N. Shank
Australasian Journal of Combinatorics 87 (2023), pp. 214–238.
arXiv
On the Domination Number of Permutation Graphs and an Application to Strong Fixed Points
T. Baren, M. Cory, M. Friedberg, P. Gardner, J. Hammer, J. Harrington, D. McGinnis, R. Waechter, and W. H. T. Wong
Journal of Discrete Applied Mathematics 288 (2021), pp. 20–34.
arXiv · DOI