The University College London (UCL) Combinatorics Seminar is held every Monday at 4–5pm during term time.

The venue for seminars this term is Room 346 at the SSEES Bulding, 14–16 Taviton Street.

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Next Speaker

• 16th March 2026 - Arjun Ranganathan (University College London)

  Exact supported co-degree bounds for Hamilton cycles

  
  

  Over recent decades, determining hypergraph extensions of Dirac’s theorem has been an extensive research theme in extremal graph theory, where the task is to determine the best possible minimum co-degree conditions that guarantee a Hamilton cycle. In this talk, we will motivate the notion of supported co-degrees, a variant of the standard co-degree notion that is particularly useful in hypergraphs with non-trivial independent sets. Our main result establishes an exact optimal bound on the minimum supported co-degree threshold for Hamilton cycles.

  Our proof splits into extremal and non-extremal regimes, and we will briefly discuss both. The latter case utilises a novel blow-up tiling framework introduced by Lang and avoids traditional approaches using the regularity and blow-up lemmas.

  This talk is based on joint work with Shoham Letzter.