Colour-blind Can Distinguish Colour Pallets

Let c : E → {1, . . . , k} be an edge colouring of a connected graph G = (V,E). Each vertex v is endowed with a naturally defined pallet under c, understood as the multiset of colours incident with v. If δ(G) > 2, we obviously (for k large enough) may colour the edges of G so that adjacent vertices are distinguished by their pallets of colours. Suppose then that our coloured graph is examined by a person who is unable to name colours, but perceives if two object placed next to each other are coloured differently. Can we colour G so that this individual can distinguish colour pallets of adjacent vertices? It is proved that if δ(G) is large enough, then it is possible using just colours 1, 2 and 3. This result is sharp and improves all earlier ones. It also constitutes a strengthening of a result by Addario-Berry, Aldred, Dalal and Reed (2005).