Asymmetric edge-colorings of graphs with three colors

An edge-coloring of a graph is called asymmetric if the only automorphism which preserves it is the identity. Lehner, Pilsniak, and Stawiski proved that all connected, locally finite, regular graphs except K2 admit an asymmetric edge-coloring with three colors. We generalize this result for graphs whose minimum degree delta and finite maximum degree increment satisfy delta > increment /2. (c) 2022 Elsevier Ltd. All rights reserved.