Perfect forests in graphs and their extensions

Gutin, Gregory; Yeo, Anders

doi:10.1002/jgt.22841

Cited by 1 publication

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References 18 publications

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“…, v n . Our construction is based on a construction from [7]. For i ∈ [n], let H i be a digraph (see Figure 1) with vertex set…”

Section: Perfect Out-forestsmentioning

confidence: 99%

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Perfect Out-forests and Steiner Cycle Packing in Digraphs

Sun¹

2022

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In this paper, we study the complexity of two types of digraph packing problems: perfect out-forests problem and Steiner cycle packing problem.For the perfect out-forest problem, we prove that it is NP-hard to decide whether a given strong digraph contains a 1-perfect outforest. However, when restricted to a semicomplete digraph D, the problem of deciding whether D contains an i-perfect out-forest becomes polynomial-time solvable, where i ∈ {0, 1}. We also prove that it is NP-hard to find a 0-perfect out-forest of maximum size in a connected acyclic digraph, and it is NP-hard to find a 1-perfect out-forest of maximum size in a connected digraph.For the Steiner cycle packing problem, when both k ≥ 2, ℓ ≥ 1 are fixed integers, we show that the problem of deciding whether there are at least ℓ internally disjoint directed S-Steiner cycles in an Eulerian digraph D is NP-complete, where S ⊆ V (D) and |S| = k. However, when we consider the class of symmetric digraphs, the problem becomes polynomial-time solvable. We also show that the problem of deciding whether there are at least ℓ arc-disjoint directed S-Steiner cycles in a given digraph D is NP-complete, where S ⊆ V (D) and |S| = k.

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“…, v n . Our construction is based on a construction from [7]. For i ∈ [n], let H i be a digraph (see Figure 1) with vertex set…”

Section: Perfect Out-forestsmentioning

confidence: 99%

“…The undirected version of i-perfect out-forest has been studied by some researchers [2,5,7,11,12]. Gutin and Yeo [6] introduced the concept of perfect out-forest in digraphs, and they did basic research on this topic by proving the NP-hardness for the problem of perfect out-forest in strong digraphs (Theorem 2.1).…”

Section: Introduction 1motivationsmentioning

confidence: 99%

Perfect Out-forests and Steiner Cycle Packing in Digraphs

Sun¹

2022

Preprint

View full text Add to dashboard Cite

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Perfect forests in graphs and their extensions

Cited by 1 publication

References 18 publications

Perfect Out-forests and Steiner Cycle Packing in Digraphs

Perfect Out-forests and Steiner Cycle Packing in Digraphs

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