Let c:E(G)→[k] be an edge-coloring of a graph G, not necessarily
proper. For each vertex v, let cˉ(v)=(a1,…,ak), where ai is
the number of edges incident to v with color i. Reorder cˉ(v) for
every v in G in nonincreasing order to obtain c∗(v), the color-blind
partition of v. When c∗ induces a proper vertex coloring, that is,
c∗(u)=c∗(v) for every edge uv in G, we say that c is color-blind
distinguishing. The minimum k for which there exists a color-blind
distinguishing edge coloring c:E(G)→[k] is the color-blind index of G,
denoted dal(G). We demonstrate that determining the
color-blind index is more subtle than previously thought. In particular,
determining if dal(G)≤2 is NP-complete. We also connect
the color-blind index of a regular bipartite graph to 2-colorable regular
hypergraphs and characterize when dal(G) is finite for a class
of 3-regular graphs.Comment: 10 pages, 3 figures, and a 4 page appendi