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.