Problem:
While I was trying to run sudo gparted, the following error occured:
X11 connection rejected because of wrong authentication. Unable to init server: Could not connect: Connection refused (gpartedbin:29293): Gtk-WARNING **: 01:55:02.070: cannot open display: localhost:10.0
Solution:
For me, the solution was to copy the .Xauthority file from the user uli I logged in as to root:
sudo cp ~$USER/.Xauthority /root
as this was required for the X11 program running as root to properly login to my local X11 server.