Snakes and Ladders: A Treewidth Story

Steven Chaplick; Steven Kelk; Ruben Meuwese; Matús Mihalák; Georgios Stamoulis

doi:10.1007/978-3-031-43380-1_14

Snakes and Ladders: A Treewidth Story

Steven Chaplick^*, Steven Kelk, Ruben Meuwese, Matús Mihalák, Georgios Stamoulis

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic

Abstract

Let G be an undirected graph. We say that G contains a ladder of length k if the (Formula presented) grid graph is an induced subgraph of G that is only connected to the rest of G via its four cornerpoints. We prove that if all the ladders contained in G are reduced to length 4, the treewidth remains unchanged (and that this bound is tight). Our result indicates that, when computing the treewidth of a graph, long ladders can simply be reduced, and that minimal forbidden minors for bounded treewidth graphs cannot contain long ladders. Our result also settles an open problem from algorithmic phylogenetics: the common chain reduction rule, used to simplify the comparison of two evolutionary trees, is treewidth-preserving in the display graph of the two trees.

Original language	English
Title of host publication	Graph-Theoretic Concepts in Computer Science - 49th International Workshop, WG 2023, Revised Selected Papers
Subtitle of host publication	49th International Workshop, WG 2023, Fribourg, Switzerland, June 28–30, 2023, Revised Selected Papers
Editors	Daniël Paulusma, Bernard Ries
Publisher	Springer, Cham
Pages	187-200
Number of pages	14
ISBN (Print)	9783031433795
DOIs	https://doi.org/10.1007/978-3-031-43380-1_14
Publication status	Published - 2023
Event	49th International Workshop on Graph-Theoretic Concepts in Computer Science - University of Fribourg, Fribourg, Switzerland Duration: 28 Jun 2023 → 30 Jun 2023 https://events.unifr.ch/wg2023/

Publication series

Series	Lecture Notes in Computer Science
Volume	14093
ISSN	0302-9743

Conference

Conference	49th International Workshop on Graph-Theoretic Concepts in Computer Science
Abbreviated title	WG 2023
Country/Territory	Switzerland
City	Fribourg
Period	28/06/23 → 30/06/23
Internet address	https://events.unifr.ch/wg2023/

Access to Document

10.1007/978-3-031-43380-1_14

https://dblp.org/rec/conf/wg/ChaplickKMMS23

1 Preprint

Snakes and Ladders: a Treewidth Story
Chaplick, S., Kelk, S., Meuwese, R., Mihalak, M. & Stamoulis, G., 21 Feb 2023.
Research output: Working paper / Preprint › Preprint

Cite this

Chaplick, S., Kelk, S., Meuwese, R., Mihalák, M., & Stamoulis, G. (2023). Snakes and Ladders: A Treewidth Story. In D. Paulusma, & B. Ries (Eds.), Graph-Theoretic Concepts in Computer Science - 49th International Workshop, WG 2023, Revised Selected Papers: 49th International Workshop, WG 2023, Fribourg, Switzerland, June 28–30, 2023, Revised Selected Papers (pp. 187-200). Springer, Cham. https://doi.org/10.1007/978-3-031-43380-1_14

Chaplick, Steven ; Kelk, Steven ; Meuwese, Ruben et al. / Snakes and Ladders: A Treewidth Story. Graph-Theoretic Concepts in Computer Science - 49th International Workshop, WG 2023, Revised Selected Papers: 49th International Workshop, WG 2023, Fribourg, Switzerland, June 28–30, 2023, Revised Selected Papers. editor / Daniël Paulusma ; Bernard Ries. Springer, Cham, 2023. pp. 187-200 (Lecture Notes in Computer Science, Vol. 14093).

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title = "Snakes and Ladders: A Treewidth Story",

abstract = "Let G be an undirected graph. We say that G contains a ladder of length k if the (Formula presented) grid graph is an induced subgraph of G that is only connected to the rest of G via its four cornerpoints. We prove that if all the ladders contained in G are reduced to length 4, the treewidth remains unchanged (and that this bound is tight). Our result indicates that, when computing the treewidth of a graph, long ladders can simply be reduced, and that minimal forbidden minors for bounded treewidth graphs cannot contain long ladders. Our result also settles an open problem from algorithmic phylogenetics: the common chain reduction rule, used to simplify the comparison of two evolutionary trees, is treewidth-preserving in the display graph of the two trees.",

author = "Steven Chaplick and Steven Kelk and Ruben Meuwese and Mat{\'u}s Mihal{\'a}k and Georgios Stamoulis",

note = "DBLP's bibliographic metadata records provided through http://dblp.org/search/publ/api are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.; 49th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2023 ; Conference date: 28-06-2023 Through 30-06-2023",

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Chaplick, S , Kelk, S , Meuwese, R , Mihalák, M & Stamoulis, G 2023, Snakes and Ladders: A Treewidth Story. in D Paulusma & B Ries (eds), Graph-Theoretic Concepts in Computer Science - 49th International Workshop, WG 2023, Revised Selected Papers: 49th International Workshop, WG 2023, Fribourg, Switzerland, June 28–30, 2023, Revised Selected Papers. Springer, Cham, Lecture Notes in Computer Science, vol. 14093, pp. 187-200, 49th International Workshop on Graph-Theoretic Concepts in Computer Science, Fribourg, Switzerland, 28/06/23. https://doi.org/10.1007/978-3-031-43380-1_14

Snakes and Ladders: A Treewidth Story. / Chaplick, Steven ; Kelk, Steven ; Meuwese, Ruben et al.
Graph-Theoretic Concepts in Computer Science - 49th International Workshop, WG 2023, Revised Selected Papers: 49th International Workshop, WG 2023, Fribourg, Switzerland, June 28–30, 2023, Revised Selected Papers. ed. / Daniël Paulusma; Bernard Ries. Springer, Cham, 2023. p. 187-200 (Lecture Notes in Computer Science, Vol. 14093).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic

TY - CHAP

T1 - Snakes and Ladders: A Treewidth Story

AU - Chaplick, Steven

AU - Kelk, Steven

AU - Meuwese, Ruben

AU - Mihalák, Matús

AU - Stamoulis, Georgios

N1 - DBLP's bibliographic metadata records provided through http://dblp.org/search/publ/api are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.

PY - 2023

Y1 - 2023

N2 - Let G be an undirected graph. We say that G contains a ladder of length k if the (Formula presented) grid graph is an induced subgraph of G that is only connected to the rest of G via its four cornerpoints. We prove that if all the ladders contained in G are reduced to length 4, the treewidth remains unchanged (and that this bound is tight). Our result indicates that, when computing the treewidth of a graph, long ladders can simply be reduced, and that minimal forbidden minors for bounded treewidth graphs cannot contain long ladders. Our result also settles an open problem from algorithmic phylogenetics: the common chain reduction rule, used to simplify the comparison of two evolutionary trees, is treewidth-preserving in the display graph of the two trees.

AB - Let G be an undirected graph. We say that G contains a ladder of length k if the (Formula presented) grid graph is an induced subgraph of G that is only connected to the rest of G via its four cornerpoints. We prove that if all the ladders contained in G are reduced to length 4, the treewidth remains unchanged (and that this bound is tight). Our result indicates that, when computing the treewidth of a graph, long ladders can simply be reduced, and that minimal forbidden minors for bounded treewidth graphs cannot contain long ladders. Our result also settles an open problem from algorithmic phylogenetics: the common chain reduction rule, used to simplify the comparison of two evolutionary trees, is treewidth-preserving in the display graph of the two trees.

U2 - 10.1007/978-3-031-43380-1_14

DO - 10.1007/978-3-031-43380-1_14

M3 - Chapter

SN - 9783031433795

T3 - Lecture Notes in Computer Science

SP - 187

EP - 200

BT - Graph-Theoretic Concepts in Computer Science - 49th International Workshop, WG 2023, Revised Selected Papers

A2 - Paulusma, Daniël

A2 - Ries, Bernard

PB - Springer, Cham

T2 - 49th International Workshop on Graph-Theoretic Concepts in Computer Science

Y2 - 28 June 2023 through 30 June 2023

ER -

Chaplick S , Kelk S , Meuwese R , Mihalák M , Stamoulis G. Snakes and Ladders: A Treewidth Story. In Paulusma D, Ries B, editors, Graph-Theoretic Concepts in Computer Science - 49th International Workshop, WG 2023, Revised Selected Papers: 49th International Workshop, WG 2023, Fribourg, Switzerland, June 28–30, 2023, Revised Selected Papers. Springer, Cham. 2023. p. 187-200. (Lecture Notes in Computer Science, Vol. 14093). doi: 10.1007/978-3-031-43380-1_14

Snakes and Ladders: A Treewidth Story

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Snakes and Ladders: a Treewidth Story

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