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Packing Arc-Disjoint 4-Cycles in Oriented Graphs

Authors Jasine Babu, R. Krithika, Deepak Rajendraprasad

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Author Details

Jasine Babu
  • Indian Institute of Technology Palakkad, India
R. Krithika
  • Indian Institute of Technology Palakkad, India
Deepak Rajendraprasad
  • Indian Institute of Technology Palakkad, India

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Jasine Babu, R. Krithika, and Deepak Rajendraprasad. Packing Arc-Disjoint 4-Cycles in Oriented Graphs. In 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 250, pp. 5:1-5:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.FSTTCS.2022.5

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • Mathematics of computing → Graph algorithms
Keywords
  • arc-disjoint cycles
  • bipartite digraphs
  • oriented graphs
  • parameterized complexity

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