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An upper bound for the twin chromatic index of a graph. (English) Zbl 1314.05038
Summary: For a connected graph \(G\) of order at least 3 and an integer \(k\geq 2\), a twin edge \(k\)-coloring of \(G\) is a proper edge coloring of \(G\) with the elements of \(\mathbb{Z}_k\) so that the induced vertex coloring in which the color of a vertex \(v\) in \(G\) is the sum (in \(\mathbb{Z}_k\)) of the colors of the edges incident with \(v\) is a proper vertex coloring. The minimum \(k\) for which \(G\) has a twin edge \(k\)-coloring is called the twin chromatic index of \(G\) and is denoted by \(\chi_t'(G)\).
In this note, we show that \(\chi_t'(G)\leq< 4\Delta(G)-3\) for every connected graph \(G\) of order at least 3.

MSC:
05C05 Trees
05C15 Coloring of graphs and hypergraphs
05C40 Connectivity
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