Erickson–Klein conjecture on weakly cordial trees

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 group $A$, the family of trees is weakly $A$-cordial. The conjecture asks whether each Abelian group admits only finitely many exceptional trees; its general status is not specified in the source.