Disjoint Paths and Connected Subgraphs for H-Free Graphs
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 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 $k \geq 1$. 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2021
- DOI:
- 10.48550/arXiv.2105.06349
- arXiv:
- arXiv:2105.06349
- Bibcode:
- 2021arXiv210506349K
- Keywords:
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- Mathematics - Combinatorics;
- Computer Science - Computational Complexity;
- Computer Science - Discrete Mathematics;
- Computer Science - Data Structures and Algorithms