Opuscula Math. 36, no. 5 (2016), 603-612
http://dx.doi.org/10.7494/OpMath.2016.36.5.603
Opuscula Mathematica
M2-edge colorings of dense graphs
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.
