The Parameterized Complexity of Cycle Packing: Indifference is Not an Issue

  • R. Krithika
  • Abhishek SahuEmail author
  • Saket Saurabh
  • Meirav Zehavi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10807)


In the Cycle Packing problem, we are given an undirected graph G, a positive integer r, and the task is to check whether there exist r vertex-disjoint cycles. In this paper, we study Cycle Packing with respect to a structural parameter, namely, distance to proper interval graphs (indifference graphs). In particular, we show that Cycle Packing is fixed-parameter tractable (FPT) when parameterized by t, the size of a proper interval deletion set. For this purpose, we design an algorithm with \(\mathcal {O}(2^{\mathcal {O}(t \log t)} n^{\mathcal {O}(1)})\) running time. Several structural parameterizations for Cycle Packing have been studied in the literature and our FPT algorithm fills a gap in the ecology of such parameterizations. We combine color coding, greedy strategy and dynamic programming based on structural properties of proper interval graphs in a non-trivial fashion to obtain the FPT algorithm.


Cycle Software Proper Interval Graphs Cycle Packing Problem Vertex-disjoint Triangles Indifference Graphs 
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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • R. Krithika
    • 1
    • 2
  • Abhishek Sahu
    • 1
    • 2
    Email author
  • Saket Saurabh
    • 1
    • 2
    • 3
  • Meirav Zehavi
    • 4
  1. 1.The Institute of Mathematical Sciences, HBNIChennaiIndia
  2. 2.UMI ReLaxChennaiIndia
  3. 3.University of BergenBergenNorway
  4. 4.Ben-Gurion UniversityBeershebaIsrael

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