Zhang–Chen–Li–Yao–Lu–Wang's adjacent vertex distinguishing total-colouring conjecture

Let $G$ be a graph, let $\Delta(G)$ be its maximum degree, and let $\chi'_{at}(G)$ be the least number of colours in a proper total colouring whose incident colour sets at adjacent vertices are distinct.

Zhang–Chen–Li–Yao–Lu–Wang's conjecture. For every graph $G$,

$$\Delta(G)+1\leq \chi'_{at}(G)\leq \Delta(G)+3.$$

The lower bound follows from the total chromatic number. A universal additive constant is known, but the specific bound $\Delta(G)+3$ remains open in general.