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Letter Graphs and Geometric Grid Classes of Permutations: Characterization and Recognition

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Combinatorial Algorithms (IWOCA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10765))

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Abstract

In this paper, we reveal an intriguing relationship between two seemingly unrelated notions: letter graphs and geometric grid classes of permutations. We also present the first constructive polynomial-time algorithm for the recognition of 3-letter graphs.

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References

  1. Albert, M.H., Atkinson, M.D., Bouvel, M., Ruskuc, N., Vatter, V.: Geometric grid classes of permutations. Trans. Am. Math. Soc. 365, 5859–5881 (2013)

    Article  MathSciNet  Google Scholar 

  2. Atminas, A., Lozin, V.: Labelled induced subgraphs and well-quasi-ordering. Order 32(3), 313–328 (2015)

    Article  MathSciNet  Google Scholar 

  3. Damaschke, P.: Induced subgraphs and well-quasi-ordering. J. Graph Theory 14(4), 427–435 (1990)

    Article  MathSciNet  Google Scholar 

  4. Fellows, M.R., Rosamond, F.A., Rotics, U., Szeider, S.: Clique-width is NP-complete. SIAM J. Discrete Math. 23(2), 909–939 (2009)

    Article  MathSciNet  Google Scholar 

  5. Korpelainen, N., Lozin, V.: Two forbidden induced subgraphs and well-quasi-ordering. Discrete Math. 311(16), 1813–1822 (2011)

    Article  MathSciNet  Google Scholar 

  6. Lampis, M.: Algorithmic meta-theorems for restrictions of treewidth. Algorithmica 64(1), 19–37 (2012)

    Article  MathSciNet  Google Scholar 

  7. Mahadev, N.V.R., Peled, U.N.: Threshold Graphs and Related Topics: Annals of Discrete Mathematics, vol. 56. North-Holland Publishing Co., Amsterdam (1995). xiv+543 pp.

    MATH  Google Scholar 

  8. Nešetřil, J.: On ordered graphs and graph orderings. Discrete Appl. Math. 51(1–2), 113–116 (1994)

    Article  MathSciNet  Google Scholar 

  9. Petkovšek, M.: Letter graphs and well-quasi-order by induced subgraphs. Discrete Math. 244, 375–388 (2002)

    Article  MathSciNet  Google Scholar 

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Acknowledgment

Vadim Lozin and Viktor Zamaraev acknowledge support of EPSRC, grant EP/L020408/1.

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Authors and Affiliations

  1. Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK

    Bogdan Alecu, Vadim Lozin & Viktor Zamaraev

  2. Institute of Mathematics, EPFL, 1015, Lausanne, Switzerland

    Dominique de Werra

Authors
  1. Bogdan Alecu
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  2. Vadim Lozin
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  3. Viktor Zamaraev
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  4. Dominique de Werra
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Corresponding author

Correspondence to Vadim Lozin .

Editor information

Editors and Affiliations

  1. University of Newcastle Australia, Callaghan, New South Wales, Australia

    Ljiljana Brankovic

  2. University of Newcastle Australia, Callaghan, New South Wales, Australia

    Joe Ryan

  3. McMaster University, Hamilton, Ontario, Canada

    William F. Smyth

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Alecu, B., Lozin, V., Zamaraev, V., de Werra, D. (2018). Letter Graphs and Geometric Grid Classes of Permutations: Characterization and Recognition. In: Brankovic, L., Ryan, J., Smyth, W. (eds) Combinatorial Algorithms. IWOCA 2017. Lecture Notes in Computer Science(), vol 10765. Springer, Cham. https://doi.org/10.1007/978-3-319-78825-8_16

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  • DOI: https://doi.org/10.1007/978-3-319-78825-8_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-78824-1

  • Online ISBN: 978-3-319-78825-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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