Publications

Peer-reviewed publications

2025

1. Rigid graphs in cylindrical normed spaces. with D. Kitson. SIAM Journal on Discrete Mathematics (accepted). http://arxiv.org/abs/2305.08421 

2. On the uniqueness of collections of pennies and marbles. with G. Grasegger, K. Kubjas, F. Mohammadi, A. Nixon. Examples and Counterexamples 7, 100181. https://doi.org/10.1016/j.exco.2025.100181

3. Single-cell 3D genome reconstruction in the haploid setting using rigidity theory. with G. Grasegger, K. Kubjas, F. Mohammadi, A. Nixon. Journal of Mathematical Biology 90, 45. https://doi.org/10.1007/s00285-025-02203-2

4. Rigid frameworks with dilation constraints. with  A. Nixon, A. Sainsbury. Discrete Mathematics 348:2, 114304. https://doi.org/10.1016/j.disc.2024.114304.

2024

5. The number of realisations of a rigid graph in Euclidean and spherical geometries. with G. Grasegger. Algebraic Combinatorics 7:6, 1615-1645. https://doi.org/10.5802/alco.390

6. Maximum likelihood thresholds via graph rigidity. with D.I. Bernstein, S.J. Gortler, A. Nixon, M. Sitharam, L. Theran. Annals of Applied Probability 14:2, 287-305. https://doi.org/10.1214/23-AAP2039 

7. Uniquely realisable graphs in analytic normed planes. with J. Hewetson, A. Nixon. International Mathematics Research Notices rnae162. https://doi.org/10.1093/imrn/rnae162 

8. Quotient graphs of symmetrically rigid frameworks. with G. Grasegger, E. Kastis, A. Nixon. Documenta Mathematica 29:3, 561-595. https://doi.org/10.4171/dm/958 

9. How many contacts can exist between oriented squares of various sizes? Discrete Mathematics 347:4, 113879. https://doi.org/10.1016/j.disc.2024.113879

2023

10. Computing maximum likelihood thresholds using graph rigidity. with D.I. Bernstein, S.J. Gortler, A. Nixon, M. Sitharam, L. Theran. Algebraic Statistics 4:2, 287–305. https://doi.org/10.2140/astat.2023.14.287

11. Coincident-point rigidity in normed planes. with J. Hewetson, A. Nixon. Ars Mathematica Contemporanea 24:1, #P1.10. https://doi.org/10.26493/1855-3974.2826.3dc

12. Graph rigidity properties of Ramanujan graphs. with S.M. Cioabă, G. Grasegger, X. Gu. The Electronic Journal of Combinatorics 30:3, #P3.12. https://doi.org/10.37236/11324

13. Classifying the globally rigid edge-transitive graphs and distance-regular graphs in the plane. Journal of Graph Theory 103:2, 175–185. https://doi.org/10.1002/jgt.22913

14. Flexing infinite frameworks with applications to braced Penrose tilings. with J. Legerský. Discrete Applied Mathematics 324, 1–17. https://doi.org/10.1016/j.dam.2022.09.002

2022

15. Infinitesimal rigidity and prestress stability for frameworks in normed spaces. Discrete Applied Mathematics 322, 425–438. https://doi.org/10.1016/j.dam.2022.09.001

16. Generalised rigid body motions in non-Euclidean planes with applications to global rigidity. with A. Nixon. Journal of Mathematical Analysis and Applications 514:1, 126259. https://doi.org/10.1016/j.jmaa.2022.126259

17. Homothetic packings of centrally symmetric convex bodies. Geometriae Dedicata 216, 11. https://doi.org/10.1007/s10711-022-00675-w

18. Flexible placements of graphs with rotational symmetry. with G. Grasegger, J. Legerský. 2nd IMA Conference on Mathematics of Robotics, 89–97. https://doi.org/10.1007/978-3-030-91352-6_9

19. Which graphs are rigid in Lpd? with D. Kitson, A. Nixon. Journal of Global Optimization 83, 49–71. https://doi.org/10.1007/s10898-021-01008-z

2021

20. Flexible placements of periodic graphs in the plane. Discrete and Computational Geometry 66, 1286–1329. https://doi.org/10.1007/s00454-021-00328-x

21. Spectral conditions for graph rigidity in the Euclidean plane. with S.M. Cioabă, X. Gu. Discrete Mathematics 344:10, 112527. https://doi.org/10.1016/j.disc.2021.112527

22. Equivalence of continuous, local and infinitesimal rigidity in normed spaces. Discrete and Computational Geometry 65, 655–679. https://doi.org/10.1007/s00454-019-00135-5

2020

23. Computing animations of linkages with rotational symmetry (media exposition). with G. Grasegger, J. Legerský. 36th International Symposium on Computational Geometry (SoCG 2020). https://doi.org/10.4230/LIPIcs.SoCG.2020.77

24. Infinitesimal rigidity in normed planes. SIAM Journal on Discrete Mathematics 34:2, 1205–1231. https://doi.org/10.1137/19M1284051

Data sets

2024

1. Non-planar graphs with various apex properties. with G. Grasegger, E. Kastis, A. Nixon, B. Servatius. Zenodo. https://doi.org/10.5281/zenodo.10671129

2. Non-planar apex graphs with different independence properties. with G. Grasegger, E. Kastis, A. Nixon, B. Servatius. Zenodo. https://doi.org/10.5281/zenodo.10671321

3. Non-planar (3,6)-sparse graphs with various apex properties. with G. Grasegger, E. Kastis, A. Nixon, B. Servatius. Zenodo. https://doi.org/10.5281/zenodo.10671293

2023

4. Marble graphs with various rigidity properties. with G. Grasegger, K. Kubjas, F. Mohammadi, A. Nixon. Zenodo. https://doi.org/10.5281/zenodo.8114283

2022

5. Ramanujan graphs with degree 3, 4, 5, 6, or 7. with S.M. Cioabă, G. Grasegger, X. Gu. Zenodo. https://doi.org/10.5281/zenodo.6579837

6. Rigidity of 4-regular Ramanujan graphs. with S.M. Cioabă, G. Grasegger, X. Gu. Zenodo. https://doi.org/10.5281/zenodo.6579718

Submitted publications

1. Uniquely realisable graphs in polyhedral normed spaces. https://arxiv.org/abs/2504.02139 

2. A tropical approach to rigidity: counting realisations of frameworks. with O. Clarke, D. Green Tripp, J. Maxwell, A. Nixon, Y. Ren, B. Smith. https://arxiv.org/abs/2502.10255 

3. Triangulated spheres with holes in triangulated surfaces. with K. Clinch, N. Fuladi, M. Gorsky, T. Huynh, E. Kastis, A. Nakamoto, A. Nixon, B. Servatius. https://arxiv.org/abs/2410.04450

4. Constructing reflection-symmetric flexible realisations of graphs. with G. Grasegger, J. Legerský. https://arxiv.org/abs/2408.06928 

5. Edge-length preserving embeddings of graphs between normed spaces. with E. Kastis, D. Kitson, W. Sims. https://arxiv.org/abs/2405.02189

6. Angular constraints on planar frameworks. with  G. Grasegger, A. Nixon, Z. Rosen, W. Sims, M. Sitharam, D. Urizar. https://arxiv.org/abs/2403.16145

7. Extremal decompositions of tropical varieties and relations with rigidity theory. with  F. Babaee, J. Maxwell. http://arxiv.org/abs/2403.00655

8. Rigidity of nearly planar classes of graphs. with  G. Grasegger, E. Kastis, A. Nixon, B. Servatius. https://arxiv.org/abs/2402.17499

9. Identifying contact graphs of sphere packings with generic radii. https://arxiv.org/abs/2302.12588