TY - GEN

T1 - DFS tree construction

T2 - 14th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 1988

AU - Korach, Ephraim

AU - Ostfeld, Zvi

N1 - Publisher Copyright:
© 1989, Springer-Verlag.

PY - 1989/1/1

Y1 - 1989/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85034834519&partnerID=8YFLogxK

U2 - 10.1007/3-540-50728-0_37

DO - 10.1007/3-540-50728-0_37

M3 - Conference contribution

AN - SCOPUS:85034834519

SN - 9783540507284

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 87

EP - 106

BT - Graph-Theoretic Concepts in Computer Science - International Workshop, WG 1988, Proceedings

A2 - van Leeuwen, J.

PB - Springer Verlag

Y2 - 15 June 1988 through 17 June 1988

ER -