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math.CO2026

Finding matchings in dense hypergraphs

Jie Han, Peter Keevash

We consider the algorithmic decision problem that takes as input an -vertex -uniform hypergraph with minimum codegree at least and decides whether it has a matching…

math.CO2024

The existence of designs

Peter Keevash

We prove the existence conjecture for combinatorial designs, answering a question of Steiner from 1853. More generally, we show that the natural divisibility conditions are suffici…

math.CO2024

Long induced paths in expanders

Nemanja Draganić, Peter Keevash

We prove that any bounded degree regular graph with sufficiently strong spectral expansion contains an induced path of linear length. This is the first such result for expanders, s…