DFS tree construction: Algorithms and characterizations: Preliminary version

Ephraim Korach; Zvi Ostfeld

doi:10.1007/3-540-50728-0_37

DFS tree construction: Algorithms and characterizations: Preliminary version

Ephraim Korach, Zvi Ostfeld

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

12 Scopus citations

Abstract

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.

Original language	English
Title of host publication	Graph-Theoretic Concepts in Computer Science - International Workshop, WG 1988, Proceedings
Editors	J. van Leeuwen
Publisher	Springer Verlag
Pages	87-106
Number of pages	20
ISBN (Print)	9783540507284
DOIs	https://doi.org/10.1007/3-540-50728-0_37
State	Published - 1 Jan 1989
Externally published	Yes
Event	14th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 1988 - Amsterdam, Netherlands Duration: 15 Jun 1988 → 17 Jun 1988

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	344 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	14th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 1988
Country/Territory	Netherlands
City	Amsterdam
Period	15/06/88 → 17/06/88

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1007/3-540-50728-0_37

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Korach, E., & Ostfeld, Z. (1989). DFS tree construction: Algorithms and characterizations: Preliminary version. In J. van Leeuwen (Ed.), Graph-Theoretic Concepts in Computer Science - International Workshop, WG 1988, Proceedings (pp. 87-106). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 344 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-50728-0_37

Korach, Ephraim ; Ostfeld, Zvi. / DFS tree construction : Algorithms and characterizations: Preliminary version. Graph-Theoretic Concepts in Computer Science - International Workshop, WG 1988, Proceedings. editor / J. van Leeuwen. Springer Verlag, 1989. pp. 87-106 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "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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Korach, E & Ostfeld, Z 1989, DFS tree construction: Algorithms and characterizations: Preliminary version. in J van Leeuwen (ed.), Graph-Theoretic Concepts in Computer Science - International Workshop, WG 1988, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 344 LNCS, Springer Verlag, pp. 87-106, 14th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 1988, Amsterdam, Netherlands, 15/06/88. https://doi.org/10.1007/3-540-50728-0_37

DFS tree construction: Algorithms and characterizations: Preliminary version. / Korach, Ephraim; Ostfeld, Zvi.
Graph-Theoretic Concepts in Computer Science - International Workshop, WG 1988, Proceedings. ed. / J. van Leeuwen. Springer Verlag, 1989. p. 87-106 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 344 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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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.

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Korach E, Ostfeld Z. DFS tree construction: Algorithms and characterizations: Preliminary version. In van Leeuwen J, editor, Graph-Theoretic Concepts in Computer Science - International Workshop, WG 1988, Proceedings. Springer Verlag. 1989. p. 87-106. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-50728-0_37

DFS tree construction: Algorithms and characterizations: Preliminary version

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