3 citations · 4 across the 7 of their papers we have counts for
9 papers · 1 filter
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 co…
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…
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…
Graphs with large minimum degree and no small odd cycles are -colourable
Julia Böttcher, Nóra Frankl, Domenico Mergoni Cecchelli +2
Answering a question by Letzter and Snyder, we prove that for large enough any -vertex graph with minimum degree at least and without odd cycles of len…
Partition universality for graphs of bounded degeneracy and degree
Peter Allen, Julia Böttcher
We prove asymptotically optimal bounds on the number of edges a graph must have in order that any -colouring of has a colour class which contains every -degenerate…
Partitioning a 2-edge-coloured graph of minimum degree into three monochromatic cycles
Peter Allen, Julia Böttcher, Richard Lang +2
Lehel conjectured in the 1970s that every red and blue edge-coloured complete graph can be partitioned into two monochromatic cycles. This was confirmed in 2010 by Bessy and Thomas…