A colouring of edges of a graph is *distingushing* if no non-identity automorphism of the graph preserves this colouring.

Problem.Is it true that each biconnected graph possesses a distinguishing colouring using $1+\lceil\Delta^{1/\delta}\rceil$ colours?

Here $\Delta$ and $\delta$ stand for the largest and smallest degree of a vertex of the graph. The colouring needs not be proper, i.e., adjacent edges can be coloured by the same colour.

A graph is *biconnected* if it remains connected after removing any vertex and its incident edges.

(The problem is posed 07.04.2018 by Imrich, Kalinowski and Pilsniak on page 21 of Volume 1 of the Lviv Scottish Book).

**Prize for solution**: Strudel i kawa przed seminarium w Katedrze matematyki dyskretnej AGH, na ktorym autor przedstawi rozwiazanie.