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Abstract: Generalizing and unifying earlier results of W. Mader and of the second and third authors, we prove two splitting theorems concerning mixed graphs. By invoking these theorems we obtain min-max formulae for the minimum number of new edges to be added to a mixed graph so that the resulting graph satisfies local edgeconnectivity prescriptions. An extension of Edmonds' theorem on disjoint arborescences is also deduced along with a new sufficient condition for the solvability of the edge-disjoint... (Update)
Context of citations to this paper: More
...the investigation of possible extensions of the basic splitting off theorems. For example, some extensions to mixed graphs are given in [1]. Another way of generalizing the splitting off results is to consider problems where not only the k edge connectivity must be preserved...
...algorithms that does not add parallel edges. Very recently this task was solved for the special cases k 5 by Taoka, Takafuji and Watanabe [1994]. The fundamental min max theorem of Watanabe and Nakamura as follows. THEOREM 5.1 The minimum number of edges whose addition makes an...
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5: fach kantenzusammenhangenden Digraphen (context) - Mader, n- - 1982
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BibTeX entry: (Update)
J. Bang-Jensen, A. Frank, B. Jackson, Preserving and increasing local edge-connectivity in mixed graphs, SIAM J. Discrete Math. 8 (1995), no. 2, 155--178. http://citeseer.ist.psu.edu/bang-jensen95preserving.html More
@article{ bangjensen95preserving,
author = "Jorgen Bang-Jensen and Andras Frank and Bill Jackson",
title = "Preserving and Increasing Local Edge-Connectivity in Mixed Graphs",
journal = "SIAM Journal on Discrete Mathematics",
volume = "8",
number = "2",
pages = "155-178",
year = "1995",
url = "citeseer.ist.psu.edu/bang-jensen95preserving.html" }
Citations (may not include all citations):126 Combinatorial Problems and Exercises (context) - Lov'asz - 1979
83 Princeton Univ (context) - Ford, Fulkerson et al. - 1962
42 Augmentation problems (context) - Eswaran, Tarjan - 1976
33 A fast algorithm for optimally increasing the edge-connectiv.. (context) - Naor, Gusfield et al. - 1990
27 A reduction method for edge-connectivity in graphs (context) - Mader - 1978
25 Edge-connectivity augmentation problems (context) - Watanabe, Nakamura - 1987
23 The minimum augmentation of any graph to k-edge-connected gr.. (context) - Cai, Sun - 1989
22 Generalized polymatroids and submodular flows (context) - Frank, Tardos - 1988
14 A minimax relation for directed graphs (context) - Lucchesi, Younger - 1978
13 How to make a digraph strongly connected (context) - Frank - 1981
11 Edge-disjoint branchings in directed multigraphs (context) - Shiloach - 1979
8 Optimal mixed graph augmentation (context) - Gusfield - 1987
7 On some connectivity properties of Eulerian graphs (context) - Lov'asz - 1976
7 a theorem of Mader (context) - Frank - 1990
7 On two min-max theorems in graph theory (context) - Lov'asz - 1976
6 and a certain polyhedra in: Combinatorial Structures and the.. (context) - Edmonds, functions - 1970
4 On connectivity properties of Eulerian digraphs (context) - Frank - 1989
4 Conference on Graph Theory (context) - Lov'asz - 1974
3 Edge-disjoint branchings in: Combinatorial Algorithms (context) - Edmonds - 1973
3 arc-connceted graphs (context) - Fulkerson, Shapley et al. - 1971
3 Some remarks on arc-connectivity (context) - Jackson - 1988
2 Minimum block containing a given graph (context) - Plesnik - 1976
2 Augmenting paths to meet edge-connectivity requirements (context) - Frank - 1992
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