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An adjacent vertex distinguishing edge coloring of a graph  G  without isolated edges is its proper edge coloring such that no pair of adjacent vertices meets the same set of colors in  G . We show that such coloring can be chosen from any set of lists associated to the edges of  G  as long as the size of every list is at least   Δ  +  C   Δ    1  2(  log  Δ  )   4   , where Δ is the maximum degree of  G  and  C  is a constant. The proof is probabilistic. The same is true in the environment of total colorings.

Asymptotically optimal bound on the adjacent vertex distinguishing edge choice number