eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-12-14
5:1
5:16
10.4230/LIPIcs.FSTTCS.2022.5
article
Packing Arc-Disjoint 4-Cycles in Oriented Graphs
Babu, Jasine
1
Krithika, R.
1
Rajendraprasad, Deepak
1
Indian Institute of Technology Palakkad, India
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol250-fsttcs2022/LIPIcs.FSTTCS.2022.5/LIPIcs.FSTTCS.2022.5.pdf
arc-disjoint cycles
bipartite digraphs
oriented graphs
parameterized complexity