13 citations · 74 across the 20 of their papers we have counts for
25 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 co…
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…
Separating the edges of a graph by a linear number of paths
Marthe Bonamy, Fábio Botler, François Dross +2
Recently, Letzter proved that any graph of order contains a collection of paths with the following property: for all distinct edges and …
The Ramsey numbers of squares of paths and cycles
Peter Allen, Domenico Mergoni Cecchelli, Barnaby Roberts +1
The square of a graph is the graph on with a pair of vertices an edge whenever and have distance or in . Given graphs and , the Rams…
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…
The square of a Hamilton cycle in randomly perturbed graphs
Julia Böttcher, Olaf Parczyk, Amedeo Sgueglia +1
We investigate the appearance of the square of a Hamilton cycle in the model of randomly perturbed graphs, which is, for a given , the union of any -vertex graph wit…