Opuscula Math. 35, no. 3 (2015), 287-291

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.

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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.
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Cite this article as:
Július Czap, A note on M2-edge colorings of graphs, Opuscula Math. 35, no. 3 (2015), 287-291, http://dx.doi.org/10.7494/OpMath.2015.35.3.287

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