The Free On-line Dictionary of Computing (30 December 2018):

depth-first search

    A graph search algorithm which extends the
   current path as far as possible before backtracking to the
   last choice point and trying the next alternative path.
   Depth-first search may fail to find a solution if it enters a
   cycle in the graph.  This can be avoided if we never extend a
   path to a node which it already contains.

   Opposite of breadth first search.  See also iterative
   deepening.

   (1995-04-19)