4 papers
On Ramsey-type problems for paths and cycles with few colour changes
Peter Allen, Julia Böttcher, Dennis Clemens +3
In 1967, Gerencser and Gyárfás determined the exact values of the two-colour Ramsey numbers of paths. In a footnote, they made the following observation: Every -edge-coloured…
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…
Blow-up lemmas for sparse graphs
Peter Allen, Julia Böttcher, Hiep Hà n +2
The blow-up lemma states that a system of super-regular pairs contains all bounded degree spanning graphs as subgraphs that embed into a corresponding system of complete pairs. Thi…
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…