License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2022.5
URN: urn:nbn:de:0030-drops-173979
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17397/
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Babu, Jasine ; Krithika, R. ; Rajendraprasad, Deepak

Packing Arc-Disjoint 4-Cycles in Oriented Graphs

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LIPIcs-FSTTCS-2022-5.pdf (0.9 MB)

Abstract

Given a directed graph G and a positive integer k, the Arc Disjoint r-Cycle Packing problem asks whether G has k arc-disjoint r-cycles. We show that, for each integer r ≥ 3, Arc Disjoint r-Cycle Packing is NP-complete on oriented graphs with girth r. When r is even, the same result holds even when the input class is further restricted to be bipartite. On the positive side, focusing on r = 4 in oriented graphs, we study the complexity of the problem with respect to two parameterizations: solution size and vertex cover size. For the former, we give a cubic kernel with quadratic number of vertices. This is smaller than the compression size guaranteed by a reduction to the well-known 4-Set Packing. For the latter, we show fixed-parameter tractability using an unapparent integer linear programming formulation of an equivalent problem.

BibTeX - Entry

@InProceedings{babu_et_al:LIPIcs.FSTTCS.2022.5,
  author =	{Babu, Jasine and Krithika, R. and Rajendraprasad, Deepak},
  title =	{{Packing Arc-Disjoint 4-Cycles in Oriented Graphs}},
  booktitle =	{42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)},
  pages =	{5:1--5:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-261-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{250},
  editor =	{Dawar, Anuj and Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/17397},
  URN =		{urn:nbn:de:0030-drops-173979},
  doi =		{10.4230/LIPIcs.FSTTCS.2022.5},
  annote =	{Keywords: arc-disjoint cycles, bipartite digraphs, oriented graphs, parameterized complexity}
}

Keywords: arc-disjoint cycles, bipartite digraphs, oriented graphs, parameterized complexity
Collection: 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)
Issue Date: 2022
Date of publication: 14.12.2022

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