On \(\mathrm{M}_f\)-edge colorings of graphs (Q2158189)

The authors define a new edge (not necessarily proper) coloring of the edges of a graph \(G\), where the only requirement is that for each vertex \(v\) of \(G\) is a prescribed maximum number \(f(v)\) of colors to be used on the edges incident to the vertex \(v\). Such an edge coloring is called an \(M_f\)-edge coloring of \(G\). Then \(\kappa_f(G)\) is defined to be the maximum number of colors used in an \(M_f\)-edge coloring of \(G\). Bounds and exact values for \(\kappa_f(G)\) are presented for various classes of graphs \(G.\)