An elementary proof of a tight $Δ+1$ bound for the additive chromatic number

An additive coloring assigns positive integer labels to the vertices of a graph so that adjacent vertices have different sums of their neighbors’ labels. The additive chromatic number $η(G)$ is the least $k$ for which labels from $[k]$ suffice. We give an elementary orientation argument proving that every finite simple graph $G$ satisfies $η(G) \leq Δ(G) + 1$.