Upcoming talks

• 8th December 2025 - Alp Müyesser (University of Oxford)

  Hamiltonicity probability of random induced subgraphs

  
  

  We show that if $G$ is a $2n$-vertex, $(n+1)$-regular graph, sampling each vertex of $G$ at independently at random with probability $p=1/2$ induces a subgraph $G_{1/2}$ with a Hamilton cycle, with probability at least $1/2$. This settles a problem of Erdős and Faudree who asked if this probability can be bounded below by an absolute constant. The result indicates a curious phase shift: if $G$ is a $2n$-vertex, $n$-regular graph, the probability that $G_{1/2}$ is Hamiltonian can be as low as $n^{-1/2}$ (consider $G=K_{n,n}$). Many open problems remain, for example, we conjecture that a similar phase shift occurs infinitely often for regular Hamiltonian graphs at much lower densities.

  Joint work with Nemanja Draganic and Peter Keevash.

  
  
  

• 12th January 2026 - Jon Noel (University of Victoria)

  Less Than Half of All Oriented Paths Are Anti-Sidorenko

  
  

  An oriented graph $H$ is "tournament anti-Sidorenko" if the number of homomorphisms from $H$ to any tournament $T$ is at most $(1/2)^{|A(H)|}|V(T)|^{|V(H)|}$. He, Mani, Nie and Tung conjectured that a random orientation of a long path is tournament anti-Sidorenko with probability at least $1/2 - o(1)$. We disprove their conjecture by proving that the probability of this event is at most $0.445 +o(1)$. Our proof uses a Central Limit Theorem of Janson and the Cramér–Wold Device from probability theory together with ideas from combinatorial limits. Joint work with Hao Chen, Felix Christian Clemen and Anastasiia Sharfenberg.

  
  
  

• 26th January 2026 - Joshua Erde (University of Birmingham)

  (Title TBA)

  
  
  
  
  

• 2nd February 2026 - Tung Nguyen (University of Oxford)

  (Title TBA)