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
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.
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- Július Czap
- Department of Applied Mathematics and Business Informatics, Faculty of Economics, Technical University of Košice, Nĕmcovej 32, 040 01 Košice, Slovakia
- Communicated by Mariusz Meszka.
- Received: 2013-10-10.
- Revised: 2014-09-23.
- Accepted: 2014-09-24.
- Published online: 2014-12-15.
