Projects

Hypergraph embeddings and decompositions

The goal of this project is to develop new theoretical foundations for embedding and decomposing hypergraphs, which shall then be applied to resolve several long-standing problems in the field. The research is funded by a Ramón y Cajal Fellowship from 2024 to 2029.

Related outcomes

With N. Sanhueza-Matamala,
Blowing up Dirac's theorem,
preprint (2024), 13 pages.
With N. Sanhueza-Matamala,
A hypergraph bandwidth theorem,
preprint (2024), 45 pages.
With S. Boyadzhiyska, A. Lo and M. Molloy
Simultaneous edge-colourings,
preprint (2024), 14 pages.

Minimum Degree Conditions for Hamilton Cycles

This project concerns the existence of Hamilton cycles and related structures in hypergraphs under minimum degree conditions. The research was funded by an MSCA Individual Fellowship from 2022 to 2024.

Related outcomes

With H. Hàn, J. Pedro Marciano, M. Pavez-Signé, N. Sanhueza-Matamala, A. Treglown and C. Zárate-Guerén,
Colour-bias perfect matchings in hypergraphs,
preprint (2024), 20 pages.
With F. Illingworth, A. Müyesser, O. Parczyk and A. Sgueglia,
Spanning spheres in Dirac hypergraphs,
preprint (2024), 20 pages.
With M. Schacht and J. Volec,
Tight Hamiltonicity from dense links of triples,
preprint (2024), 17 pages.
With F. Joos and N. Sanhueza-Matamala,
Robust Hamiltonicity,
preprint (2023), 30 pages.
With J. D. Alvarado, Y. Kohayakawa, G. O. Mota and H. Stagni,
Resilience for Loose Hamilton Cycles,
preprint (2023), 33 pages.
Lecture notes on the Absorption Method,
based on the course given at the 1ª Escola Brasileira de Combinatória (2023).
Tiling dense hypergraphs,
preprint (2023), 35 pages.

Large Substructures in Hypergraphs

In this project, we investigate the emergence of large substructure in graphs and hypergraphs. The research was funded by a DFG Walter Benjamin fellowship from 2020 to 2022.

Related outcomes

With P. Allen, J. Böttcher, J. Skokan and M. Stein,
Partitioning a 2-edge-coloured graph of minimum degree 2n/3 + o(n) into three monochromatic cycles,
European Journal of Combinatorics (2023), 30 pages.
By P. Arras,
Ore- and Pósa-type conditions for partitioning 2-edge-coloured graphs into monochromatic cycles,
Electronic Journal of Combinatorics (2023), 25 pages.
With E. Hurley and F. Joos,
Sufficient conditions for perfect mixed tilings,
to appear in Journal of Combinatorial Theory, Series B, 34 pages.
With N. Sanhueza-Matamala,
On sufficient conditions for spanning structures in dense graphs,
Proceedings of the London Mathematical Society (2023), 83 pages.

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