8 papers
Dirac subgraphs of powers of cycles are Hamiltonian
Richard Lang, Alp Müyesser, Mathias Schacht +1
We show that, for every and all sufficiently large , any spanning subgraph of the th power of a cycle with minimum degree at least contains…
The Lovász conjecture holds for moderately dense Cayley graphs
Benjamin Bedert, Nemanja DraganiÄ, Alp Müyesser +1
We show that there is an absolute constant such that every large connected -vertex Cayley graph with degree has a Hamilton cycle. This makes progress towar…
Towards Graham's rearrangement conjecture via rainbow paths
Matija BuciÄ, Bryce Frederickson, Alp Müyesser +2
We study an old question in combinatorial group theory which can be traced back to a conjecture of Graham from 1971. Given a group , and some subset , is it poss…
On the Graham--Sloane harmonious labelling conjecture
Alp Müyesser, Alexey Pokrovskiy
Consider an order abelian group and a tree on vertices. When is it possible to (bijectively) label by so that along all edges of , the sums …
On Graham's rearrangement conjecture over
Benjamin Bedert, Matija BuciÄ, Noah Kravitz +2
A sequence of elements of a group is called a valid ordering if the partial products are all distinct. A long-standi…
New bounds for linear arboricity and related problems
Micha Christoph, Nemanja DraganiÄ, António Girão +3
A linear forest is a collection of vertex-disjoint paths. The Linear Arboricity Conjecture states that every graph of maximum degree can be decomposed into at most $\lceil(Î+…