A maze with n walls is homeomorphic to the n-times punctured plane. So the method of cuts used by Cauchy to derive a simply-connected domain can be applied. The cuts in this instance become barriers joining the walls in some sequence, the last one getting a final barrier going off to infinity. Then any two points in the maze can be joined by a path which is homotopically unique, the possibility of going round in circles being eliminated.
  The method of Tremaux noted in the Wikipedia Maze article may amount to the same thing but with the barriers introduced on the run rather than in advance.

  Copyright Dec04 conesetter. Quotation with acknowledgement psrmitted.