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An edge-coloring of a loopless plane graph G is a facial rainbow edge-coloring if any two edges of G contained in the same facial path have distinct colors. The facial rainbow edge-number of a graph G, denoted $$\mathrm {erb}(G)$$ erb(G) , is the minimum number of colors that are necessary in any facial rainbow edge-coloring. In the present note we prove that $$\mathrm {erb}(G) \le \lfloor \frac{3}{2}...
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