Opuscula Math. 35, no. 3 (2015), 287-291
http://dx.doi.org/10.7494/OpMath.2015.35.3.287

Opuscula Mathematica

# A note on M2-edge colorings of graphs

Július Czap

Abstract. An edge coloring $$\varphi$$ of a graph $$G$$ is called an $$M_2$$-edge coloring if $$|\varphi(v)|\le2$$ for every vertex $$v$$ of $$G$$, where $$\varphi(v)$$ is the set of colors of edges incident with $$v$$. Let $$K_2(G)$$ denote the maximum number of colors used in an $$M_2$$-edge coloring of $$G$$. Let $$G_1$$, $$G_2$$ and $$G_3$$ be graphs such that $$G_1\subseteq G_2\subseteq G_3$$. In this paper we deal with the following question: Assuming that $$K_2(G_1)=K_2(G_3)$$, does it hold $$K_2(G_1)=K_2(G_2)=K_2(G_3)$$?

Keywords: edge coloring, graph.

Mathematics Subject Classification: 05C15.

Full text (pdf)