Edge-disjoint in- and out-branchings in tournaments and related path problems

Bang‐Jensen, Jørgen

doi:10.1016/0095-8956(91)90002-2

Cited by 49 publications

(76 citation statements)

References 6 publications

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“…This problem is easily seen to be NP-complete, since there is a trivial reduction of the 2-path problem to this problem. It was shown in [10] that in the case of arc-disjoint paths the characterization for semicomplete digraphs given in [5] still holds for quasi-transitive digraphs and locally in-semicomplete digraphs. In the case of internally vertex-disjoint paths (i.e., when we want an (x, z)-path that passes through y) it was pointed out in [10] that the complete characterization for semicomplete digraphs given in [4] is also valid for quasi-transitive digraphs.…”

Section: Disjoint Pathsmentioning

confidence: 98%

Generalizations of tournaments: A survey

Bang‐Jensen¹,

Gutin

1998

J. Graph Theory

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We survey results concerning various generalizations of tournaments. The reader will see that tournaments are by no means the only class of directed graphs with a very rich structure. We describe, among numerous other topics mostly related to paths and cycles, results on hamiltonian paths and cycles. The reader will see that although these problems are polynomially solvable for all of the classes described, they can be highly non-trivial, even for these "tournament-like" digraphs.

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Section: Disjoint Pathsmentioning

confidence: 98%

Generalizations of tournaments: A survey

Bang‐Jensen¹,

Gutin

1998

J. Graph Theory

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“…Given this result, a natural question is whether in polynomial time one can find an out-branching and an in-branching that are arc-disjoint. However, it is NP-complete to decide whether a given digraph has a pair of arc-disjoint branchings B + s , B − t [2]. In fact, as was shown recently by two of the authors, this already holds for 2-regular digraphs [4].…”

Section: Introductionmentioning

confidence: 87%

Parameterized Algorithms for Non-separating Trees and Branchings in Digraphs

2015

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A well known result in graph algorithms, due to Edmonds, states that given a digraph D and a positive integer , we can test whether D contains arc-disjoint out-branchings in polynomial time. However, if we ask whether there exists an outbranching and an in-branching which are arc-disjoint, then the problem becomes NP-complete. In fact, even deciding whether a digraph D contains an out-branching which is arc-disjoint from some spanning tree in the underlying undirected graph remains NP-complete. In this paper we formulate some natural optimization questions around these problems and initiate its study in the realm of parameterized complexity. More precisely, the problems we study are the following: Arc-Disjoint Branchings and Non-Disconnecting Out-Branching. In Arc-Disjoint Branchings (NonDisconnecting Out-Branching), a digraph D and a positive integer k are given as input and the goal is to test whether there exist an out-branching and in-branching (respectively, a spanning tree in the underlying undirected graph) that differ on at least k arcs. We obtain the following results for these problems.• Non-Disconnecting Out-Branching is fixed parameter tractable (FPT) and admits a linear vertex kernel. • Arc-Disjoint Branchings is FPT on strong digraphs. 123 AlgorithmicaThe algorithm for Non-Disconnecting Out-Branching runs in time 2 O(k) n O(1) and the approach we use to obtain this algorithms seems useful in designing other moderately exponential time algorithms for edge/arc partitioning problems.

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“…v) be the in-neighbor (resp. out-neighbor) of h in P 1 , let a be a vertex of H. As the arcs ua, av must be in A(D), the path P 1 := P 1 …”

Section: Lemma 23 Let D Be a Digraph A List Of K Terminal Pairs Anmentioning

confidence: 99%

Arc-Disjoint Paths in Decomposable Digraphs

Bang‐Jensen

Maddaloni

2013

J. Graph Theory

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Abstract:We prove that the weak k-linkage problem is polynomial for every fixed k for totally -decomposable digraphs, under appropriate hypothesis on . We then apply this and recent results by Fradkin and Seymour (on the weak k-linkage problem for digraphs of bounded independence number or bounded cut-width) to get polynomial algorithms for some classes of digraphs like quasi-transitive digraphs, extended semicomplete digraphs, locally semicomplete digraphs (all of which contain the class of semicomplete digraphs as a subclass) and directed cographs. C 2013 Wiley Periodicals, Inc.

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Edge-disjoint in- and out-branchings in tournaments and related path problems

Cited by 49 publications

References 6 publications

Generalizations of tournaments: A survey

Generalizations of tournaments: A survey

Parameterized Algorithms for Non-separating Trees and Branchings in Digraphs

Arc-Disjoint Paths in Decomposable Digraphs

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