3 problems

Hovey's cordial labelling conjecture. Every tree admits a labelling by $\mathbb{Z}_k$, for every $k$, such that each vertex label occurs either $s$ or $s+1$ times and each edge lab…

Let $A$ be an Abelian group. A family of graphs is weakly $A$-cordial if all but finitely many graphs in the family are $A$-cordial. Erickson–Klein conjecture. For every Abelian gr…

Beasley's conjecture. Every orientation of every path is $(2,3)$-cordial except for a path with four vertices, and every tree of maximum degree $3$ is $(2,3)$-orientable.