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Branchwidth is ( 1, g )-self-dual

Published: 09 July 2024 Publication History

Abstract

A graph parameter is self-dual in some class of graphs embeddable in some surface if its value does not change in the dual graph by more than a constant factor. We prove that, in the class of connected hypergraphs without bridges and loops that are embeddable in some surface of Euler genus at most g, branchwidth is a ( 1, g )-self-dual parameter, i.e., for every hypergraph G in the class, the branchwidth of its dual is at most the branchwidth of G plus g. This is the first proof that branchwidth is an additively self-dual width parameter.

References

[1]
Amini Omid, Huc Florian, Pérennes Stéphane, On the path-width of planar graphs, SIAM J. Discrete Math. 23 (3) (2009) 1311–1316.
[2]
Barrière Lali, Flocchini Paola, Fomin Fedor V., Fraigniaud Pierre, Nisse Nicolas, Santoro Nicola, Thilikos Dimitrios M., Connected graph searching, Inf. Comput. 219 (2012) 1–16.
[3]
Bodlaender Hans L., Fomin Fedor V., Approximation of pathwidth of outerplanar graphs, J. Algorithms 43 (2) (2002) 190–200.
[4]
Bouchitté Vincent, Mazoit Frédéric, Todinca Ioan, Chordal embeddings of planar graphs, Discrete Math. 273 (1) (2003) 85–102.
[5]
Coudert David, Huc Florian, Sereni Jean-Sébastien, Pathwidth of outerplanar graphs, J. Graph Theory 55 (1) (2007) 27–41.
[6]
Fomin Fedor V., Thilikos Dimitrios M., On self duality of pathwidth in polyhedral graph embeddings, J. Graph Theory 55 (1) (2007) 42–54.
[7]
Geelen James F., Gerards Albertus M.H., Whittle Geoff, Branch-width and well-quasi-ordering in matroids and graphs, J. Combin. Theory Ser. B 84 (2) (2002) 270–290.
[8]
Gu Qian-Ping, Tamaki Hisao, Optimal branch-decomposition of planar graphs in O(n3) time, ACM Trans. Algorithms 4 (3) (2008) 30:1–30:13.
[9]
Hicks Illya V., McMurray Nolan B., The branchwidth of graphs and their cycle matroids, J. Combin. Theory Ser. B 97 (5) (2007) 681–692.
[10]
Kashyap Navin, Matroid pathwidth and code trellis complexity, SIAM J. Discrete Math. 22 (1) (2008) 256–272.
[11]
Koutsonas Athanassios, Thilikos Dimitrios M., Yamazaki Koichi, Outerplanar obstructions for matroid pathwidth, Discrete Math. 315–316 (2014) 95–101.
[12]
Lapoire Denis, Treewidth and duality for planar hypergraphs, 1996, Manuscript.
[13]
Mäkinen Erkki, How to draw a hypergraph, Int. J. Comput. Math. 34 (3–4) (1990) 177–185.
[14]
Mazoit Frédéric, Décomposition Algorithmique des Graphes, (Ph.D. thesis) École Normale Supérieure de Lyon, 2004.
[15]
Mazoit Frédéric, Tree-width of graphs and surface duality, J. Combin. Theory Ser. B 102 (3) (2012) 671–687.
[16]
Mazoit Frédéric, Thomassé Stéphan, Branchwidth of graphic matroids, in: Surveys in Combinatorics 2007, in: London Mathematical Society Lecture Note Series, Vol. 346, Cambridge University Press, 2007, pp. 275–286.
[17]
Mohar Bojan, Thomassen Carsten, Graphs on Surfaces, John Hopkins University Press, 2001.
[18]
Oxley James, Matroid Theory, in: Oxford Graduate Texts in Mathematics, Vol. 21, second ed., Oxford University Press, Oxford, 2011, p. xiv+684.
[19]
Robertson Neil, Seymour Paul D., Graph minors. III. Planar tree-width, J. Combin. Theory Ser. B 36 (1984) 49–64.
[20]
Robertson Neil, Seymour Paul D., Graph minors. X. Obstructions to tree-decomposition, J. Combin. Theory Ser. B 52 (2) (1991) 153–190.
[21]
Robertson Neil, Seymour Paul D., Graph minors. XX. Wagner’s conjecture, J. Combin. Theory Ser. B 92 (2) (2004) 325–357. Special Issue Dedicated to Professor W.T. Tutte.
[22]
Sau Ignasi, Thilikos Dimitrios M., On self-duality of branchwidth in graphs of bounded genus, Discrete Appl. Math. 159 (17) (2011) 2184–2186.
[23]
Seymour Paul D., Thomas Robin, Call routing and the ratcatcher, Combinatorica 14 (2) (1994) 217–241.
[24]
Vatshelle Martin, New Width Parameters of Graphs, (Ph.D. thesis) University of Bergen, 2012.

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Published In

cover image Discrete Applied Mathematics
Discrete Applied Mathematics  Volume 350, Issue C
Jun 2024
123 pages

Publisher

Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 09 July 2024

Author Tags

  1. Branchwidth
  2. Duality
  3. Self-dual parameters
  4. Surface-embeddable graphs
  5. Matroid branchwidth

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