J. Edmonds, "Edge-disjoint branchings, combinatorial algorithms," Combinatorial Algorithms, R. Rustin, ed., New York, Algorithmic Press, 1972. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Broadcasting on Uni-directional Hypercubes and Its Applications - Huang, Yang, Tseng (2003) (Correct)
.... resulting subgraph is still connected (strongly connected) 2] An algorithm for communicating in a digraph D(V, A) can tolerate f faults if and only if each data element can be routed through at least f 1 node disjoint paths from its source to its destination [11] It has been proven by Edmonds [10] that every digraph possesses as many arc disjoint spanning trees rooted at any node as the arc connectivity of the digraph. Here, for a digraph D = V, A) arc connectivity represents the minimum number of elements in an arc set A such that D = V, A A ) is not a strongly connected digraph. ....
J. Edmonds, "Edge-disjoint branchings, combinatorial algorithms," Combinatorial Algorithms, R. Rustin, ed., New York, Algorithmic Press, 1972.
Connectivity Augmentation - Frank (1994) (Correct)
....are minimal with respect to edge deletion. The main observation is that such digraphs are precisely those in which (a) the in degree of every node v 6= s is precisely k and (b) the underlining undirected graph is the union of k disjoint spanning trees. The equivalence may be proved by Edmonds [1973] disjoint arborescence theorem) By this equivalent formulation the problem is to find a minimum cost common basis of two matroids M 1 and M 2 defined on the edge set of D. Here M 1 is a partition matroid in which a set is independent if contains at most k edges entering any node v 6= s. M 2 is ....
....k connectivity augmentation problem also has a solution. Unfortunately, at present, it is not known if the problem is NP complete or it is perhaps in co NP NP or even in P. 17 For general k, F. Harary [1962] found the solution when the starting graph has n nodes but no edges. Wang and Kleitman [1973] determined a necessary and sufficient condition for the existence of a k connected graph with specified degree sequence. For general starting graphs, solutions are known only for small k. When k = 1 the problem is obvious. Plesnik [1976] and Eswaran and Tarjan [1976] proved a min max formula for ....
J. Edmonds, Edge-disjoint branchings in: Combinatorial Algorithms (B. Rustin, ed.), Acad. Press, New York, (1973), 91-96.
Preserving And Increasing Local Edge-Connectivity In.. - Bang-Jensen, Frank.. (1995) (Correct)
.... we are given a subset T U Gamma z so that (X) k for every subset X U Gamma z; X T 6= Is it true that there are k disjoint arborescences so that each contains every element of T The answer is yes if T = U Gamma z (by Edmonds theorem) or if jT j = 1 (by Menger s theorem) But Lov asz [1973] found the the following example to show that such a statement is not true in general. Figure 2.1 Here k = 2, T consists of three nodes and there are no two disjoint arborescences both containing every element of T . Observe that (x) 1 ffi (x) 2 holds for the only node x not in T . In this ....
J. Edmonds, Edge-disjoint branchings in: Combinatorial Algorithms (B. Rustin, ed.), Acad. Press, New York, (1973), 91-96.
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