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math.CO2025
Bounds for Hypergraph Universality
Peter Allen, Julia Böttcher, Jasmin Katz
A graph is said to be universal for a class of graphs if contains a copy of every as a subgraph. The number of edges required for a host g…
math.CO2025
Robustness of the Sauer-Spencer Theorem
Peter Allen, Julia Böttcher, Yoshiharu Kohayakawa +1
We prove a robust version of a graph embedding theorem of Sauer and Spencer. To state this sparser analogue, we define to be a random subgraph of obtained by retaining e…
math.CO2025
Ramsey numbers for 1-degenerate 3-graphs
Peter Allen, Simona Boyadzhiyska, Matías Pavez-Signé
We construct a 3-uniform 1-degenerate hypergraph on vertices whose 2-colour Ramsey number is . This shows that all remaining open cases of the hyperg…