Opuscula Math. 36, no. 5 (2016), 603-612

Opuscula Mathematica

M2-edge colorings of dense graphs

Jaroslav Ivančo

Abstract. An edge coloring \(\varphi\) of a graph \(G\) is called an \(\mathrm{M}_i\)-edge coloring if \(|\varphi(v)|\leq i\) for every vertex \(v\) of \(G\), where \(\varphi(v)\) is the set of colors of edges incident with \(v\). Let \(\mathcal{K}_i(G)\) denote the maximum number of colors used in an \(\mathrm{M}_i\)-edge coloring of \(G\). In this paper we establish some bounds of \(\mathcal{K}_2(G)\), present some graphs achieving the bounds and determine exact values of \(\mathcal{K}_2(G)\) for dense graphs.

Keywords: edge coloring, dominating set, dense graphs.

Mathematics Subject Classification: 05C15.

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  • Jaroslav Ivančo
  • Institute of Mathematics, P. J. Šafárik University, Jesenná 5, 041 54 Košice, Slovakia
  • Communicated by Mariusz Meszka.
  • Received: 2015-06-19.
  • Revised: 2016-02-24.
  • Accepted: 2016-02-24.
  • Published online: 2016-06-29.
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Cite this article as:
Jaroslav Ivančo, M2-edge colorings of dense graphs, Opuscula Math. 36, no. 5 (2016), 603-612, http://dx.doi.org/10.7494/OpMath.2016.36.5.603

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