On Mf-Edge Colorings of Graphs
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-e...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2022-11-01
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| Series: | Discussiones Mathematicae Graph Theory |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgt.2329 |
| Summary: | 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. |
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| ISSN: | 2083-5892 |