The large-shift conjecture for graphs without isolated $P_2$ components

Let $G$ be a graph, and let $k$ be an integer. A $k$-shifted-antimagic labeling of $G$ is an injective edge labeling by the consecutive integers $k+1,k+2,\ldots,k+|E(G)|$ such that all vertex sums are distinct. Large-shift conjecture. Every graph is $k$-shifted-antimagic for $|k|$ sufficiently large if it does not contain a component isomorphic to $P_2$. The paper notes that existence of such labelings for graphs with mixed even degrees is still unknown, and presents this assertion as a proposed direction for future work.