L. Lovasz, On two min-max theorems in graph theory, JCT Series B, 21 (1976) 96-103. Home/Search Document Not in Database Summary Related Articles Check |
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Connectivity Augmentation - Frank (1994) (Correct)
....functions (established in [Edmonds and Giles, 1977] extends this theorem to the weighted case. In [Frank, 1981a] a strongly polynomial time algorithm was developed to find the minimum in question. The augmentation problem for strong connectivity was solved by K.P. Eswaran and R.E. Tarjan [1976] in the case when any possible new edge is allowed to be added and c j 1. In a digraph the sink sets are closed under taking intersection and union. Hence the minimal sink sets (with respect to containment) are pairwise disjoint. Let p 1 denote their number. Similarly, the minimal source sets are ....
....technique to make the algorithm of Watanabe and Nakamura strongly polynomial. The first strongly polynomial algorithm [Frank 1992] for the k edge connectivity augmentation problem followed a different line. One of its basic ideas, the use of splitting off technique, was suggested by Plesnik [1976] when k = 2 and by Cai and Sun [1989] for arbitrary k 2. Using splitting off is equivalent to use degree prescribed augmentation problems. THEOREM 5.4 Let G = V; E) be an undirected graph and m a non negative integer valued function on V . G can be made k edge connected (k 2) by adding a set F ....
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L. Lov'asz, On two min-max theorems in graph theory, J. Combinatorial Theory, Ser. B, 21 (1976) 26-30.
Minimal Edge-Coverings of Pairs of Sets - Frank, Jordán (1995) (15 citations) (Correct)
....an explanation why (apart from results including parity considerations) a great part of min max theorems in graph theory and combinatorial optimization, especially those involving subor supermodular functions, are implied by the models above. But not all For example, K.P. Eswaran and R.E. Tarjan [1976] proved a min max theorem for the minimum number of new edges whose addition makes a given directed graph strongly connected. They also observed that the minimum cost version of this problem is NP complete as it includes the directed Hamiltonian circuit problem. Therefore, though the proof of this ....
....the present section is to show that the corresponding node connectivity augmentation problems can also be solved with the help of our general model. When k = 1, k edge connectivity and k node connectivity coincide. The minimization problem for this case was solved by K.P. Eswaran and R.E. Tarjan [1976] while the feasibility form follows from Mader s result. For larger k only very little was known. The minimization form was solved by [Masuzawa et al. 1987] when the starting digraph D is an arborescence (that is, a directed tree in which every node is reachable from a root. T. Jord an [1993b] ....
L. Lov'asz, On two min-max theorems in graph theory, J. Combinatorial Theory, Ser. B, 21 (1976) 26-30.
Applications Of Submodular Functions - Frank (1993) (6 citations) (Correct)
....of the preceding problem; that is, improve a digraph by adding a minimum cost set of new edges so as to have k openly disjoint paths from a specified source node to each other node. The problem was solved in [Frank and Tardos 1989] with the help of submodular flows. K.P. Eswaran and R.E. Tarjan [1976] described a method of making a digraph strongly connected by adding a minimum number of edges. They also noticed that the minimum cost version of this problem includes as a special case the directed Hamiltonian path problem and therefore is NP complete. However, the problem is tractable if we are ....
....value of an admissible sub partition. We have and although equality does not hold in general, in important special cases it does. For a subset A T the notation (A; T Gamma A; G) will be abbreviated to (A; G) or to (A) when no confusion can arise. B.V. Cherkasskij [1977] and L. Lov asz [1976] proved the following theorem: THEOREM 7.7 For an inner Eulerian pair (G; T ) the maximum number of edge disjoint T paths is equal to ( P (t) t 2 T ) 2. Furthermore, there is a family of disjoint sets fX(t) t 2 Tg such that t 2 X(t) V and dG (X t ) t) t 2 T ) 18 An equivalent ....
L. Lov'asz, On two min-max theorems in graph theory, J. Combinatorial Theory, Ser. B, 21 (1976) 26-30.
Finding small k-arc-strong Spanning Subdigraphs in.. - Bang-Jensen, Huang, Yeo (2000) (Correct)
....D 0 be the spanning subdigraph of D induced by the arc set of these 2k branchings. Then jA(D 0 )j 2k(n Gamma 1) and for every v 2 V (D) Gamma r we have D 0 (r; v) k and D 0 (v; r) k. Now it is an easy exercise, using Menger s theorem, to prove that D 0 is k arc strong. Pi Lov asz [16] gave a constructive proof of Theorem 3.1, which can easily be turned into a polynomial algorithm to find k arc disjoint out branchings with the same root or detect that no such set of branchings exist in a given digraph D with a specified vertex r. Hence we have the following corollary: ....
L. Lov'asz, On two min--max theorems in graph theory, J. Combin. Theory Ser. B 21 (1976) 26-30.
Directed Network Design with Orientation Constraints - Khanna, Naor, Shepherd (2000) (2 citations) (Correct)
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L. Lovasz, On two min-max theorems in graph theory, JCT Series B, 21 (1976) 96-103.
Directed Network Design with Orientation Constraints - Khanna, Naor, Shepherd (2000) (2 citations) (Correct)
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L. Lov'asz, On two min-max theorems in graph theory, JCT Series B, 21 (1976) 96-103. 13
Preserving And Increasing Local Edge-Connectivity In.. - Bang-Jensen, Frank.. (1995) (Correct)
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L. Lov'asz, On two min-max theorems in graph theory, J. Combinatorial Theory, Ser. B, 21 (1976) 26-30.
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