5 papers
Embedding trees using minimum and maximum degree conditions
Alexey Pokrovskiy, Leo Versteegen, Ella Williams
A variant of the Erdős-Sós conjecture, posed by Havet, Reed, Stein and Wood, states that every graph with minimum degree at least and maximum degree at least…
Relative Turán densities for ordered graphs: all and nothing
Freddie Illingworth, Arjun Ranganathan, Leo Versteegen +1
Reiher, Rödl, Sales, and Schacht initiated the study of relative Turán densities of ordered graphs and showed that it is more subtle and interesting than the unordered case. For an…
On the gracesize of trees
Shoham Letzter, Alexey Pokrovskiy, Ella Williams
An -vertex tree is said to be if there exists a bijective labelling such that the edge-differences $\{|ϕ(x)-ϕ(y)| : xy\in E(T)…
A proof of a conjecture of Erdős and Gyárfás on monochromatic path covers
Alexey Pokrovskiy, Leo Versteegen, Ella Williams
In 1995, Erdős and Gyárfás proved that in every -edge-coloured complete graph on vertices, there exists a collection of monochromatic paths, all of the same colo…
Towards an edge-coloured Corrádi--Hajnal theorem
Allan Lo, Ella Williams
A classical result of Corrádi and Hajnal states that every graph on vertices with and contains a perfect triangle-tiling, i.e.,\ a spanni…