Disjoint Paths and Connected Subgraphs for H-Free Graphs
Combinatorics
2021-05-14 v1 Computational Complexity
Discrete Mathematics
Data Structures and Algorithms
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 -free graphs. If is fixed, we obtain the -Disjoint Paths problem, which is known to be polynomial-time solvable on the class of all graphs for every . 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 -Disjoint Connected Subgraphs for -free graphs, and give the same almost-complete classification for Disjoint Connected Subgraphs for -free graphs as for Disjoint Paths.
Cite
@article{arxiv.2105.06349,
title = {Disjoint Paths and Connected Subgraphs for H-Free Graphs},
author = {Walter Kern and Barnaby Martin and Daniël Paulusma and Siani Smith and Erik Jan van Leeuwen},
journal= {arXiv preprint arXiv:2105.06349},
year = {2021}
}