North Tyrol borders Salzburg in the east , the German state of Bavaria in the north , Vorarlberg in the west , the Swiss canton of GraubÃ 1\/4 nden in the southwest and Bolzano-Bozen in the south . North Tyrol borders Salzburg in the east , the German federal-state of Bavaria in the north , Vorarlberg to the west , the Swiss canton of GraubÃ 1\/4 nden ( Grison ) to the southwest and the Italian Province of Bolzano-Bozen in the south .