Ella Williams

Embedding trees using minimum and maximum degree conditions

A variant of the notable Erdős–Sós conjecture, posed by Havet, Reed, Stein and Wood, states that every graph with minimum degree at least 2k/3 and maximum degree at least k contains a copy of every tree with k edges. Both of these bounds are best possible. For large trees with bounded maximum degree, we prove this exactly. We also prove similar, approximate results for related conjectures, where alternative degree combinations are considered. Joint work with Alexey Pokrovskiy and Leo Versteegen.