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Katherine Staden

Katherine Staden

Senior Lecturer

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mathematics-and-statistics

Professional biography

I am a senior lecturer in pure maths in the School of Mathematics and Statistics; I joined the OU in January 2022. I was an undergraduate at Trinity Hall, University of Cambridge, and received a PhD from the University of Birmingham in 2015, followed by postdoctoral research at Warwick and Oxford.

Research interests

I am interested in combinatorics (discrete mathematics); in particular extremal and probabilistic combinatorics. Recently I've been working on graph decompositions and some problems in extremal graph theory.

I am a member of the OU combinatorics and algebra group.

My work is supported by a UKRI Future Leaders Fellowship (2025-29).

Publications

All my papers are available on ArXiv.

Submitted papers

  1. 'Rainbow subgraphs of star-coloured graphs' (with A. Lo, K. Markström, D. Mubayi, M. Stein and L. Weber), 2025, arXiv:2511.12505. (32pp)

  2. 'The semi-inducibility problem’ (with A. Basit, B. Granet, D. Horsley and A. Kündgen), 2025, arxiv:2501.09842. (43pp)

  3. 'A framework for the generalised Erdős-Rothschild problem and a resolution of the dichromatic triangle case’ (with P. Gupta, Y. Pehova and E. Powierski), 2025, arXiv:2502.12291. (58pp)

Published papers

  1. 'Transversals via regularity’ (with Y. Cheng), 2026, J. Combin. Theory B, pp. 498-550.

  2. 'Geometric constructions for Ramsey-Turán theory’ (with H. Liu, C. Reiher, M. Sharifzadeh), 2025, J. European Math. Soc., online first (27pp)

  3. 'Stability of transversal Hamilton cycles and paths’ (with Y. Cheng), 2025, Elec. J. Combin. 32, Paper 4.36 (35pp)

  4. 'Ringel’s tree-packing conjecture in quasirandom graphs’ (with P. Keevash), 2023, J. European Math. Soc., to appear. (58pp) 

  5. 'Universality for transversal Hamilton cycles’ (with C. Bowtell, P. Morris and Y. Pehova), 2025, Bull. London Math. Soc. 57 (3), pp. 711-729.

  6. 'Exact results for the Erdős-Rothschild problem’ (with O. Pikhurko), 2023, Forum Math Sigma 12, E8. (45pp) 

  7. 'Stability for the Erdős-Rothschild problem’ (with O. Pikhurko), 2023, Forum Math., Sigma 11, E23. (43pp) 

  8. 'Stability from symmetrisation arguments with applications to inducibility’ (with H. Liu, O. Pikhurko and M. Sharifzadeh), 2023, J. London Math. Soc., 108 (2), 1121-1162. 

  9. 'The generalised Oberwolfach problem’ (with P. Keevash), 2022, J. Combin. Theory B 152, pp. 281-318. 

  10. 'On the maximum number of integer colourings with forbidden monochromatic sums’ (with H. Liu and M. Sharifzadeh), 2021, Elec. J. Combin., 28 (1), P1.59. (35pp) 

  11. 'The bandwidth theorem for locally dense graphs’ (with A. Treglown), 2020, Forum Math. Sigma 8, E42. (36pp) 

  12. ‘The exact minimum number of triangles in graphs of given order and size’ (with H. Liu and O. Pikhurko), 2020, Forum Math. Pi 8, E8. (144pp) 

  13. 'Minimum number of additive tuples in groups of prime order’ (with O. Chervak and O. Pikhurko), 2019, Elec. J. Combin. 26 Paper 1.30. (16pp) 

  14. 'Independent sets in hypergraphs and Ramsey properties of graphs and the integers’ (with R. Hancock and A. Treglown), 2019, SIAM J. Disc. Math. 33, pp. 153-188. 

  15. 'Proof of Komlós’s conjecture on Hamiltonian subsets’ (with J. Kim, H. Liu and M. Sharifzadeh), 2017, Proc. London Math. Soc. 115 (5), pp. 974-1013. 

  16. 'The Erdős-Rothschild problem on edge-colourings with forbidden monochromatic cliques’ (with O. Pikhurko and Z.B. Yilma), 2017, Math. Proc. Cambridge Phil. Soc. 163, pp. 341-356. 'Local conditions for exponentially many subdivisions’ (with H. Liu and M. Sharifzadeh), 2017, Combin. Probab. Comput. 26 (3), pp. 423-430. 

  17. 'On degree sequences forcing the square of a Hamilton cycle’ (with A. Treglown), 2017, SIAM J. Disc. Math. 31 (1), pp. 383-437. 

  18. 'Solution to a problem of Bollobás and Häggkvist on Hamilton cycles in regular graphs’ (with D. Kühn, A. Lo, D. Osthus), 2016, J. Combin. Theory B 121 (Special issue, ‘Fifty Years of the Journal of Combinatorial Theory’), pp. 85-145. 

  19. 'The robust component structure of dense regular graphs and applications’ (with D. Kühn, A. Lo, D. Osthus), 2015, Proc. London Math. Soc. 110 (1), pp. 19-56. 

  20. 'Approximate Hamilton decompositions of robustly expanding regular digraphs’ (with D. Osthus), 2013, SIAM J. Disc. Math., 27 (3), pp. 1372-1409.