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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 Bucić, 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 Draganić, 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(Δ+1)…
Cyclic subsets in regular Dirac graphs
Nemanja Draganić, Peter Keevash, Alp Müyesser
In 1996, in his last paper, Erdős asked the following question that he formulated together with Faudree: is there a positive such that any -regular graph on ver…
Towards Graham's rearrangement conjecture via rainbow paths
Matija Bucić, 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 possib…