@article { ,
title = {Steiner Trees for Hereditary Graph Classes: a Treewidth Perspective},
abstract = {We consider the classical problems (Edge) Steiner Tree and Vertex Steiner Tree after restricting the input to some class of graphs characterized by a small set of forbidden induced subgraphs. We show a dichotomy for the former problem restricted to -free graphs and a dichotomy for the latter problem restricted to H-free graphs. We find that there exists an infinite family of graphs H such that Vertex Steiner Tree is polynomial-time solvable for H-free graphs, whereas there exist only two graphs H for which this holds for Edge Steiner Tree (assuming ). We also find that Edge Steiner Tree is polynomial-time solvable for -free graphs if and only if the treewidth of the class of -free graphs is bounded (subject to ). To obtain the latter result, we determine all pairs for which the class of -free graphs has bounded treewidth.},
doi = {10.1016/j.tcs.2021.03.012},
issn = {0304-3975},
journal = {Theoretical Computer Science},
note = {EPrint Processing Status: Full text deposited in DRO},
pages = {30-39},
publicationstatus = {Published},
publisher = {Elsevier},
url = {https://durham-repository.worktribe.com/output/1245461},
volume = {867},
keyword = {Algorithms and Complexity in Durham (ACiD)},
year = {2021},
author = {Bodlaender, H.L. and Brettell, N. and Johnson, M. and Paesani, G. and Paulusma, D. and van Leeuwen, E.J.}
}