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Abstract: We consider the problem (MSSS) of finding a strongly connected spanning subgraph with the minimum number of arcs in a strongly connected digraph. This problem is NP-hard for general digraphs since it generalizes the hamiltonian cycle problem. We show that the problem is polynomially solvable for quasi-transitive digraphs. We describe the minimum number of arcs in such a spanning subgraph of a quasi-transitive digraph in terms of the path covering number. Our proofs are based on a number of... (Update)
Context of citations to this paper: More
.... Recently it was shown that the MSSS problem is solvable in polynomial time for several classes which contain tournaments as a subclass [4, 5]. In the last section of this paper we also discuss briefly some approximation algorithms for this problem for general digraphs. Suppose...
...can be solved e#ciently for a much larger superclass of semicomplete digraphs than just quasi transitive digraphs. We remark that in [9], the MSSS problem was solved for various generalizations of tournaments. In particular polynomial algorithms were given for the classes of...
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Spanning k-arc-strong Subdigraphs with few arcs in.. - Bang-Jensen, Huang, Yeo (2001) (Correct)
Strongly Connected Spanning Subgraphs With the Minimum.. - Bang-Jensen, Yeo (2000) (Correct)
Strongly Connected Spanning Subgraphs with the Minimum.. - Bang-Jensen, Huang, Yeo (2000) (Correct)
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0.8: On the Complexity of Hamiltonian Path and Cycle Problems in .. - Bang-Jensen, Gutin (1997) (Correct)
0.6: Connected (g,f)-Factors and Supereulerian Digraphs - Gutin (Correct)
0.6: Generalizations of tournaments: A survey - Bang-Jensen, Gutin (1996) (Correct)
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0.4: Cycles in Semicomplete Multipartite Digraphs - Yeo (1996) (Correct)
0.3: Sufficient Conditions for Semicomplete Multipartite.. - Guo, Tewes, Volkmann.. (1997) (Correct)
0.3: A polynomial algorithm for the Hamiltonian cycle problem.. - Bang-Jensen, Gutin, Yeo (1996) (Correct)
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6: Generalizations of tournaments: a survey - Bang-Jensen, Gutin - 1998
6: An algorithm for finding a minimal equivalent graph of a digraph (context) - Hsu - 1975
6: The Transitive Reduction of a Directed Graph (context) - Aho, Garey et al. - 1972
BibTeX entry: (Update)
J. Bang-Jensen, J. Huang and A. Yeo, Strongly connected spanning subgraphs with the minimum number of arcs in quasi-transitive digraphs, submitted. http://citeseer.ist.psu.edu/article/bang-jensen99strongly.html More
@techreport{ bangjensen99strongly,
author = "Jørgen Bang-Jensen and Jing Huang and Anders Yeo",
title = "Strongly Connected Spanning Subgraphs with the Minimum Number of Arcs in Quasi-transitive Digraphs",
number = "PP-1999-05",
month = "9,",
year = "1999",
url = "citeseer.ist.psu.edu/article/bang-jensen99strongly.html" }
Citations (may not include all citations):537 Graph Theory with Applications (context) - Bondy, Murty - 1976
62 The transitive reduction of a directed graph (context) - Aho, Garey et al. - 1972 DBLP
28 Computing of maximum cardinality matching in a bipartite gra.. (context) - Alt, Blum et al. - 1991
27 Magnanti and J (context) - Ahuja - 1993
15 Quasi-transitive digraphs (context) - Bang-Jensen, Huang - 1995 ACM
13 Approximating the minimum equivalent digraph - Khuller, Raghavachari et al. - 1995 ACM DBLP
12 On strongly connected digraphs with bounded cycle length - Khuller, Raghavachari et al. - 1996 ACM DBLP
11 An algorithm for finding a minimal equivalent graph of a dig.. (context) - Hsu - 1975
11 Polynomial algorithms for finding hamiltonian paths and cycl.. (context) - Gutin - 1994
9 Transitive compaction in parallel via branchings (context) - Gibbons, Karp et al. ACM DBLP
7 Houri, Caract (context) - Ghouila- - 1962
6 A polynomial algorithm for the Hamiltonian cycle problem in .. (context) - Bang-Jensen, Gutin et al. - 1998 ACM
6 Cycles and paths in complete multipartite digraphs (context) - Gutin - 1995
6 Vertex heaviest paths and cycles in quasi-transitive digraph.. (context) - Bang-Jensen, Gutin - 1996 ACM
6 How close to regular must a semicomplete multipartite digrap.. - Yeo
5 Generalizations of tournaments: A survey (context) - Bang-Jensen, Gutin - 1998 ACM
2 Strongly connected spanning subgraphs with the minimum numbe.. (context) - Bang-Jensen, Yeo ACM
2 the complexity of hamiltonian path and cycle problems in cer.. (context) - Bang-Jensen, Gutin
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