Path-based dfs views depth-first search as maintaining a path, rather than building a depth-first spanning tree. This leads to simplified algorithms for problems such as These applications and others are discussed on these web pages.

The advantage of path-based dfs is simplicity -- the dfs path captures the structure of many problems, without need for the more complicated dfs tree. A corresponding disadvantage is that more intricate problems (for instance planarity testing) require the full power of the dfs tree.

Path-based dfs is a natural concept, dating from 19th century work on threading mazes (Tremaux's algorithm and others).