The Slovenian Mountain Trail is a route of about 600km from Maribor to Ankaran. It covers most of the Slovenian mountain areas including Pohorje, Julian Alps, Kamnik-Savinja Alps, Karavanke and the southwestern part of Slovenia. It is the oldest hiking track in Europe.
An interactive map of the route is here. It typically is done from NE to SW.
Klemen Triler and Marjan Zupančič have traded the FKT back and forth since Triler set the FKT at 8d14h45m in 2012. This video on Triler's run gives a sense of the variety of terrain along the route.
A detailed description of a route is here (in Slovenian), with maps of each daily stage from Triler's run.
Thanks Petra Pirc for pointing out these records and translation of the information.