The path partition problem and related problems in bipartite graphs

Monnot, Jérôme; Toulouse, Sophie

doi:10.1016/j.orl.2006.12.004

Cited by 61 publications

(52 citation statements)

References 13 publications

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“…On the boundary to NP-hardness, we strengthen a result of Ma lafiejski anḋ Zyliński [14] and Monnot and Toulouse [15] by showing that P 3 -Partition, which is Star Partition with s = 2, is NP-complete on grid graphs with maximum degree three. Note that in strong contrast to this, K 3 -Partition is linear-time solvable on graphs with maximum degree three [16].…”

Section: Star Partitionsupporting

confidence: 76%

“…As Kirkpatrick and Hell [12] established the NP-completeness of H-Partition on general graphs for every connected pattern H with at least three vertices, one branch of research has turned to the investigation of classes of specially structured graphs. For instance, on the upside H-Partition has been shown to be polynomial-time solvable on trees and series-parallel graphs [21] and on graphs of maximum degree two [15]. On the downside, P k -Partition (for fixed k ≥ 3) remains NP-complete on planar bipartite graphs [9]; this hardness result generalizes to H-Partition on planar graphs for any outerplanar pattern H with at least three vertices [2].…”

Section: Star Partitionmentioning

confidence: 99%

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Star Partitions of Perfect Graphs

Bevern

Bredereck

Bulteau

et al. 2014

Automata, Languages, and Programming

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Bevern, van, R.; Bredereck, R.; Bulteau, L.; Chen, J.; Froese, V.; Niedermeier, R.; Woeginger, G.Published: 01/01/2014 Document VersionPublisher's PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication:• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Abstract The partition of graphs into nice subgraphs is a central algorithmic problem with strong ties to matching theory. We study the partitioning of undirected graphs into stars, a problem known to be NP-complete even for the case of stars on three vertices. We perform a thorough computational complexity study of the problem on subclasses of perfect graphs and identify several polynomial-time solvable and NP-hard cases, for example, on interval graphs, grid graphs, and bipartite permutation graphs.

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Section: Star Partitionsupporting

confidence: 76%

Section: Star Partitionmentioning

confidence: 99%

Star Partitions of Perfect Graphs

Bevern

Bredereck

Bulteau

et al. 2014

Automata, Languages, and Programming

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“…However, we consider bipartite graphs. For this purpose, a result by Monnot and Toulouse [18] is of importance for us. Here, P k denotes a path on k vertices.…”

Section: Classifying the S(k Kℓ )-Factor Problemmentioning

confidence: 97%

“…First, Monnot and Toulouse [18] researched path factors in bipartite graphs and showed that the K 2,1 -Factor problem stays NP-complete when restricted to the class of bipartite graphs. Second, we observed that in fact the proof of the NP-completeness result for S(K 2,2 )-Factor in [14] is even a proof for bipartite graphs.…”

Section: − → H Locally Bijective Homomorphisms Have Applications In mentioning

confidence: 99%

Packing Bipartite Graphs with Covers of Complete Bipartite Graphs

Chalopin

Paulusma

2010

Lecture Notes in Computer Science

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Publisher's copyright statement:Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. For a set S of graphs, a perfect S-packing (S-factor) of a graph G is a set of mutually vertexdisjoint subgraphs of G that each are isomorphic to a member of S and that together contain all vertices of G. If G allows a covering (locally bijective homomorphism) to a graph H, i.e., a vertex mapping f : V G → V H satisfying the property that f (u)f (v) belongs to E H whenever the edge uv belongs to E G such that for every u ∈ V G the restriction of f to the neighborhood of u is bijective, then G is an H-cover. For some fixed H let S(H) consist of all connected H-covers. Let K k,ℓ be the complete bipartite graph with partition classes of size k and ℓ, respectively. For all fixed k, ℓ ≥ 1, we determine the computational complexity of the problem that tests whether a given bipartite graph has a perfect S(K k,ℓ )-packing.Our technique is partially based on exploring a close relationship to pseudo-coverings. A pseudo-covering from a graph G to a graph H is a homomorphism from G to H that becomes a covering to H when restricted to a spanning subgraph of G. We settle the computational complexity of the problem that asks whether a graph allows a pseudo-covering to K k,ℓ for all fixed k, ℓ ≥ 1.

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“…Researchers have also studied the problem of location tracking (Yavas et al, 2005;Tsai et al, 2007;Tseng & Lu, 2009) and resource allocation (Huang & Lin, 2008;Huang et al, 2003;Peng & Chen, 2005;. Bipartite graph matching is also used to find mobile user movement behavior (Ilyas et al, 2004;Fayyazi et al, 2004;Monnot & Toulouse, 2007). Currently, different approaches are in progress to find interesting patterns of mobile users Lancieri & Durand, 2006;Tseng et al, 2007;Terziyan & Vitko, 2003;Huang et al, 2003).…”

Section: Introductionmentioning

confidence: 99%