Disjoint Paths and Connected Subgraphs for H-Free Graphs.

Walter Kern; Barnaby Martin; Daniël Paulusma; Siani Smith; Erik Jan van Leeuwen

doi:10.1007/978-3-030-79987-8_29

Disjoint Paths and Connected Subgraphs for H-Free Graphs.

Walter Kern, Barnaby Martin, Daniël Paulusma, Siani Smith, Erik Jan van Leeuwen

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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≥ 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.

Original language	English
Title of host publication	Combinatorial Algorithms - 32nd International Workshop, IWOCA 2021, Ottawa, ON, Canada, July 5-7, 2021, Proceedings
Editors	Paola Flocchini, Lucia Moura
Publisher	Springer
Pages	414-427
Number of pages	14
ISBN (Print)	9783030799861
DOIs	https://doi.org/10.1007/978-3-030-79987-8_29
Publication status	Published - 2021

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12757 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Bibliographical note

Funding Information:
D. Paulusma?Supported by the Leverhulme Trust (RPG-2016-258).

Publisher Copyright:
© 2021, Springer Nature Switzerland AG.

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Kern2021_Chapter_DisjointPathsAndConnectedSubgrFinal published version, 367 KBLicence: Taverne

https://dblp.org/rec/conf/iwoca/KernMPSL21

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Kern, W., Martin, B., Paulusma, D., Smith, S., & Leeuwen, E. J. V. (2021). Disjoint Paths and Connected Subgraphs for H-Free Graphs. In P. Flocchini, & L. Moura (Eds.), Combinatorial Algorithms - 32nd International Workshop, IWOCA 2021, Ottawa, ON, Canada, July 5-7, 2021, Proceedings (pp. 414-427). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12757 LNCS). Springer. https://doi.org/10.1007/978-3-030-79987-8_29

Kern, Walter ; Martin, Barnaby ; Paulusma, Daniël et al. / Disjoint Paths and Connected Subgraphs for H-Free Graphs. Combinatorial Algorithms - 32nd International Workshop, IWOCA 2021, Ottawa, ON, Canada, July 5-7, 2021, Proceedings. editor / Paola Flocchini ; Lucia Moura. Springer, 2021. pp. 414-427 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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≥ 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.",

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Kern, W, Martin, B, Paulusma, D, Smith, S & Leeuwen, EJV 2021, Disjoint Paths and Connected Subgraphs for H-Free Graphs. in P Flocchini & L Moura (eds), Combinatorial Algorithms - 32nd International Workshop, IWOCA 2021, Ottawa, ON, Canada, July 5-7, 2021, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12757 LNCS, Springer, pp. 414-427. https://doi.org/10.1007/978-3-030-79987-8_29

Disjoint Paths and Connected Subgraphs for H-Free Graphs. / Kern, Walter; Martin, Barnaby; Paulusma, Daniël et al.
Combinatorial Algorithms - 32nd International Workshop, IWOCA 2021, Ottawa, ON, Canada, July 5-7, 2021, Proceedings. ed. / Paola Flocchini; Lucia Moura. Springer, 2021. p. 414-427 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12757 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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Kern W, Martin B, Paulusma D, Smith S, Leeuwen EJV. Disjoint Paths and Connected Subgraphs for H-Free Graphs. In Flocchini P, Moura L, editors, Combinatorial Algorithms - 32nd International Workshop, IWOCA 2021, Ottawa, ON, Canada, July 5-7, 2021, Proceedings. Springer. 2021. p. 414-427. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-79987-8_29

Disjoint Paths and Connected Subgraphs for H-Free Graphs.

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