Abstract
The well-known DISJOINT PATHS problem is to decide if a graph contains k pairwise disjoint paths, each connecting a different terminal pair from a set of k distinct vertex pairs. We determine, with an exception of two cases, the complexity of the DISJOINT PATHS problem for H-free graphs. If k is fixed, we obtain the k-DISJOINT PATHS problem, which is known to be polynomial-time solvable on the class of all graphs for every k≥1. The latter does no longer hold if we need to connect vertices from terminal sets instead of terminal pairs. We completely classify the complexity of k-DISJOINT CONNECTED SUBGRAPHS for H-free graphs, and give the same almost-complete classification for DISJOINT CONNECTED SUBGRAPHS for H-free graphs as for DISJOINT PATHS. Moreover, we give exact algorithms for DISJOINT PATHS and DISJOINT CONNECTED SUBGRAPHS on graphs with n vertices and m edges that have running times of O(2nn2k) and O(3nkm), respectively.
Original language | English |
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Pages (from-to) | 59-68 |
Number of pages | 10 |
Journal | Theoretical Computer Science |
Volume | 898 |
DOIs | |
Publication status | Published - 4 Jan 2022 |
Bibliographical note
Funding Information:Daniël Paulusma was supported by the Leverhulme Trust (RPG-2016- 258).
Publisher Copyright:
© 2021 Elsevier B.V.
Keywords
- Complexity dichotomy
- Disjoint paths
- H-free graph