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International Conference on Innovations and Interdisciplinary Solutions for Underserved Areas

InterSol 2020: Innovations and Interdisciplinary Solutions for Underserved Areas pp 238–250Cite as

On the Treewidth of Planar Minor Free Graphs

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Abstract

We study in this article, the treewidth of planar graphs excluding as minor a fixed planar graph. We prove that the treewidth of every planar graph excluding a graph having a poly-line \(p \times q\)-grid drawing is \(O(p\sqrt{q})\). As consequences, the treewidth of planar graphs excluding as minor the cylinder \(\mathscr {C}_{2,r}\) or its dual \(\mathscr {C}^*_{2,r}\) is \(O(\sqrt{r})\), where \(\mathscr {C}_{2,r}\) denotes the cylinder of height 2 and circumference r. This bound is asymptotically optimal. The treewidth is \(O(\sqrt{r\log {r}})\) if the excluded graph is any outerplanar graph with r vertices.

The work of Cyril Gavoille is partially funded by the French ANR projects ANR-16-CE40-0023 (DESCARTES) and ANR-17-CE40-0015 (DISTANCIA).

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Notes

  1. 1.

    It is well-known the \(p\times q\) grid has treewidth \(\min \{{p,q}\}\).

  2. 2.

    Note that if a triangle is chosen as outerface of \(\mathscr {C}_{3,r+2}\), then the resulting drawing has \(r+2\) nested triangles. However, a drawing with the minimal number of nested disjoint cycles can be obtained by choosing a quadrangle of \(\mathscr {C}_{3,r+2}\) as outerface.

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Author information

Authors and Affiliations

  1. LI3, Assane Seck University of Ziguinchor, Ziguinchor, Senegal

    Youssou Dieng

  2. LaBRI, University of Bordeaux, Bordeaux, France

    Cyril Gavoille

Authors
  1. Youssou Dieng
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  2. Cyril Gavoille
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Correspondence to Youssou Dieng .

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Editors and Affiliations

  1. African Climate and Development Initiative, University of Cape Town, Cape Town, South Africa

    Jessica P. R. Thorn

  2. Université Alioune Diop de Bambey, Bambey, Senegal

    Assane Gueye

  3. Department of Animal and Plant Sciences, University of Sheffield, Sheffield, UK

    Adam P. Hejnowicz

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Dieng, Y., Gavoille, C. (2020). On the Treewidth of Planar Minor Free Graphs. In: Thorn, J., Gueye, A., Hejnowicz, A. (eds) Innovations and Interdisciplinary Solutions for Underserved Areas. InterSol 2020. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 321. Springer, Cham. https://doi.org/10.1007/978-3-030-51051-0_17

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