Geodesic
On Mf-Edge Colorings of Graphs
Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 4, pp. 1075-1088

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An edge coloring φ of a graph G is called an Mf-edge coloring if |φ(v)| ≤ f(v) for every vertex v of G, where φ(v) is the set of colors of edges incident with v and f is a function which assigns a positive integer f(v) to each vertex v. Let Kf (G) denote the maximum number of colors used in an Mf-edge coloring of G. In this paper we establish some bounds on Kf(G), present some graphs achieving the bounds and determine exact values of Kf(G) for some special classes of graphs.
Keywords: edge coloring, anti-Ramsey number, dominating set 
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     title = {On {M\protect\textsubscript{f}-Edge} {Colorings} of {Graphs}},
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Ivančo, Jaroslav; Onderko, Alfréd. On Mf-Edge Colorings of Graphs. Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 4, pp. 1075-1088. http://geodesic.mathdoc.fr/item/DMGT_2022_42_4_a3/