A note on M2-edge colorings of graphs
Július Czap · Opuscula Mathematica · 2014
An edge coloring ϕ of a graph G is called an M2-edge coloring if |ϕ(v)| ≤ 2 for every vertex v of G, where ϕ(v) is the set of colors of edges incident with v. Let K2(G) denote the maximum number of colors used in an M2-edge coloring of G. Let G1, G2 and G3 be graphs such that G1 ⊆ G2 ⊆ G3.In this paper we deal with the following question: Assuming that K2(G1) = K2(G3), does it hold K2(G1) = K2(G2) = K2(G3)?