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Steiner trees for hereditary graph classes.

Bodlaender, H. and Brettell, N. and Johnson, M. and Paesani, G. and Paulusma, D. and van Leeuwen, E.J. (2020) 'Steiner trees for hereditary graph classes.', in LATIN 2020: Theoretical Informatics. , pp. 613-624. Lecture Notes in Computer Science., 14th Latin American Symposium, São Paulo, Brazil, January 5-8, 2021, Proceedings


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 (H1,H2) -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. We also find that Edge Steiner Tree is polynomial-time solvable for (H1,H2) -free graphs if and only if the treewidth of the class of (H1,H2) -free graphs is bounded (subject to P≠NP ). To obtain the latter result, we determine all pairs (H1,H2) for which the class of (H1,H2) -free graphs has bounded treewidth.

Item Type:Book chapter
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Publisher statement:The final authenticated version is available online at
Date accepted:11 February 2020
Date deposited:26 April 2020
Date of first online publication:03 December 2020
Date first made open access:21 January 2021

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