Hovey's 3-cordiality conjecture

A graph $G$ is 3-cordial if its vertices are labeled by $0$, $1$, and $2$ with label-class sizes differing by at most one, and each edge receives the sum of its endpoint labels modulo $3$, with edge-label class sizes also differing by at most one. Hovey's conjecture. All graphs are $3$-cordial. This is a special case of the $k$-cordial labeling problems introduced by Hovey; its status is not specified in the source.