DFS tree construction: Algorithms and characterizations

Preliminary version
  • Ephraim Korach
  • Zvi Ostfeld
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 344)


The Depth First Search (DFS) algorithm is one of the basic techniques which is used in a very large variety of graph algorithms. Every application of the DFS involves, beside traversing the graph, constructing a special structured tree, called a DFS tree. In this paper, we give a complete characterization of all the graphs in which every spanning tree is a DFS tree. These graphs are called Total-DFS-Graphs. The characterization we present shows that a large variety of graphs are not Total-DFS-Graphs, and therefore the following question is naturally raised: Given an undirected graph G=(V,E) and an undirected spanning tree T, is T a DFS tree of G? We give an algorithm to answer this question in linear (O(|E|)) time.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Ephraim Korach
    • 1
  • Zvi Ostfeld
    • 1
  1. 1.Computer Science DepartmentTechnion - Israel Institute of TechnologyHaifaIsrael

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