Chordless Cycle Packing Is Fixed-Parameter Tractable

Author Dániel Marx

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Dániel Marx
  • CISPA Helmholtz Center for Information Security, Saarbrücken, Germany


The author is very grateful to O-joung Kwon and Eun Jung Kim for helpful comments on the manuscript.

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Dániel Marx. Chordless Cycle Packing Is Fixed-Parameter Tractable. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 71:1-71:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


A chordless cycle or hole in a graph G is an induced cycle of length at least 4. In the Hole Packing problem, a graph G and an integer k is given, and the task is to find (if exists) a set of k pairwise vertex-disjoint chordless cycles. Our main result is showing that Hole Packing is fixed-parameter tractable (FPT), that is, can be solved in time f(k)n^O(1) for some function f depending only on k.

Subject Classification

ACM Subject Classification
  • Theory of computation → Data structures design and analysis
  • Theory of computation → Graph algorithms analysis
  • chordal graphs
  • packing
  • fixed-parameter tractability


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