The conflict-free chromatic index is at most (1+o(1)) log₂ Δ for any graph and this bound is tight.
Bollobás, The evolution of sparse graphs, in Graph Theory and Combinatorics., Proc
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Asymptotically Tight Bound for the Conflict-Free Chromatic Index
The conflict-free chromatic index is at most (1+o(1)) log₂ Δ for any graph and this bound is tight.