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Packing arc-disjoint cycles in oriented graphs

Published: 09 July 2024 Publication History

Abstract

Arc-Disjoint Cycle Packing is a classical NP-complete problem and we study it from two perspectives: (1) by restricting the cycles in the packing to be of a fixed length, and (2) by restricting the inputs to bipartite tournaments. Focusing first on Arc-Disjoint r -Cycle Packing (where the cycles in the packing are required to be of length r), we show NP-completeness in oriented graphs with girth r for each r ≥ 3 and study the parameterized complexity of the problem with respect to two parameterizations (solution size and vertex cover size) for r = 4 in oriented graphs. Moving on to Arc-Disjoint Cycle Packing in bipartite tournaments, we show that every bipartite tournament either contains k arc-disjoint cycles or has a feedback arc set of size at most 7 ( k − 1 ). This result adds to the set of Erdös-Pósa-type results known in the combinatorics literature for packing and covering problems.

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Published In

cover image Journal of Computer and System Sciences
Journal of Computer and System Sciences  Volume 143, Issue C
Aug 2024
61 pages

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Academic Press, Inc.

United States

Publication History

Published: 09 July 2024

Author Tags

  1. Arc-disjoint cycles
  2. Parameterized algorithms
  3. Kernels
  4. Erdös-Pósa-type theorems

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