4 papers · 1 filter
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…
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…