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References

Published online by Cambridge University Press:  16 May 2024

Reinhard Diestel
Reinhard Diestel
Affiliation:
Universität Hamburg
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Tangles
A Structural Approach to Artificial Intelligence in the Empirical Sciences
 , pp. 273 - 276
Publisher: Cambridge University Press
Print publication year: 2024

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References

Tangles: e-book and software. Home page at tangles-book.com.Google Scholar
Bergen, H.v.. Abstract tangle-tree duality. In preparation, 2023.Google Scholar
Bergen, H.v. and Diestel, R.. Traits and tangles: an analysis of the Big Five paradigm by tangle-based clustering. In preparation.Google Scholar
Carmesin, J., Diestel, R., Hamann, M., and Hundertmark, F.. Canonical tree-decompositions of finite graphs II. Essential parts. J. Comb. Theory Ser. B, 118:268–283, 2016.CrossRefGoogle Scholar
Carmesin, J., Diestel, R., Hamann, M., and Hundertmark, F.. Canonical tree-decompositions of finite graphs I. Existence and algorithms. J. Comb. Theory Ser. B, 116:1–24, 2016; arXiv:1406.3797.CrossRefGoogle Scholar
Carmesin, J., Diestel, R., Hundertmark, F., and Stein, M.. Connectivity and tree structure in finite graphs. Combinatorica, 34(1):1–35, 2014; arXiv:1105.1611.CrossRefGoogle Scholar
Diestel, R.. Graph Theory (5th edition). Springer-Verlag, 2017. Electronic edition available at http://diestel-graph-theory.com/.CrossRefGoogle Scholar
Diestel, R.. Tree sets. Order, 35:171–192, 2018.CrossRefGoogle Scholar
Diestel, R.. Abstract separation systems. Order, 35:157–170, 2018; arXiv:1406.3797.CrossRefGoogle Scholar
Diestel, R., Elbracht, C., and Jacobs, R.W.. Point sets and functions inducing tangles of set separations, 2021. arXiv:2107.01087; to appear in Journal of Combinatorics.Google Scholar
Diestel, R., Erde, J., Elbracht, C., and Teegen, M.. Duality and tangles of set partitions. J. Combinatorics, 15(1):1–39, 2024; arXiv:2109.08398.Google Scholar
Diestel, R., Erde, J., and Weißauer, D.. Structural submodularity and tangles in abstract separation systems. J. Comb. Theory Ser. A, 167C:155–180, 2019; arXiv:1805.01439.CrossRefGoogle Scholar
Diestel, R., Hundertmark, F., and Lemanczyk, S.. Profiles of separations: in graphs, matroids, and beyond. Combinatorica, 39(1):37–75, 2019; arXiv:1110.6207.CrossRefGoogle Scholar
Diestel, R. and Oum, S.. Tangle-tree duality in graphs, matroids and beyond. Combinatorica, 39:879–910, 2019. arXiv:1701.02651.CrossRefGoogle Scholar
Diestel, R. and Oum, S.. Tangle-tree duality in abstract separation systems. Advances in Mathematics, 377:107470, 2021; arXiv:1701.02509.CrossRefGoogle Scholar
Diestel, R. and Whittle, G.. Tangles and the Mona Lisa. arXiv:1603.06652.Google Scholar
Elbracht, C. and Kneip, J.. A canonical tree-of-tangles theorem for structurally submodular separation systems. Combinatorial Theory, 1(5), 2021.CrossRefGoogle Scholar
Elbracht, C., Kneip, J., and Teegen, M.. A note on generic tangle algorithms. arXiv:2005.14648.Google Scholar
Elbracht, C., Kneip, J., and Teegen, M.. Tangles are decided by weighted vertex sets. Advances in Comb., 2020:9, 2020; arXiv:1811.06821.Google Scholar
Elbracht, C., Kneip, J., and Teegen, M.. Trees of tangles in abstract separation systems. J. Comb. Theory Ser. A, 180:105425, 2021; arXiv:1909.09030.CrossRefGoogle Scholar
Elbracht, C., Kneip, J., and Teegen, M.. Obtaining trees of tangles from tangle-tree duality. J. Combinatorics, 13:251–287, 2022; arXiv:2011.09758.CrossRefGoogle Scholar
Ganter, Bernhard and Wille, Rudolf. Formal Concept Analysis. Springer, 1999.CrossRefGoogle Scholar
Godsil, C. and Royle, G.. Algebraic Graph Theory. Springer-Verlag, 2001.CrossRefGoogle Scholar
Grohe, Martin and Schweitzer, Pascal. Computing with tangles. In Proceedings of the Forty-seventh Annual ACM Symposium on Theory of Computing, STOC ’15, pages 683–692, New York, NY, USA, 2015. ACM.CrossRefGoogle Scholar
Hermann, M. and Bergen, H.v.. Matrix-based order functions for set partitions and functions. In preparation.Google Scholar
Hundertmark, F.. Profiles. An algebraic approach to combinatorial connectivity. arXiv:1110.6207, 2011.Google Scholar
Kelmans, Alexander K. and Kimelfeld, Boris N.. Multiplicative submodularity of a matrix’s principal minor as a function of the set of its rows and some combinatorial applications. Discrete Math., 44(1):113–116, 1983.CrossRefGoogle Scholar
Klepper, S., Elbracht, C., Fioravanti, D., Kneip, J., Rendsburg, L., Teegen, M., and Luxburg, U.v.. Clustering with tangles: Algorithmic framework and theoretical guarantees. Journal of Machine Learning Research, 24:1–56, 2023; arXiv:2006.14444.Google Scholar
Luxburg, U.v.. A tutorial on spectral clustering. Statistics and Computing, 17(4), 2007. arXiv:0711.0189.Google Scholar
Oum, Sang-il and Seymour, Paul. Approximating clique-width and branchwidth. J. Comb. Theory Ser. B, 96(4):514–528, 2006.CrossRefGoogle Scholar
Robertson, N. and Seymour, P.D.. Graph minors I–XX. J. Comb. Theory Ser. B, 1983–2004.Google Scholar
Robertson, N. and Seymour, P.D.. Graph minors. X. Obstructions to tree-decomposition. J. Comb. Theory Ser. B, 52:153–190, 1991.CrossRefGoogle Scholar
Shi, J. and Malik, J.. Normalized cuts and image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(8):888–905, 2000.Google Scholar
Wei, Y.C. and Cheng, C.K.. Towards efficient hierarchical designs by ratio cut partitioning. Proc. IEEE Int. Conf. on Computer-Aided Design, pages 298–301, 1989.Google Scholar
Wittgenstein, Ludwig. Philosophical Investigations. Basil Blackwell, Oxford, 1953.Google Scholar
Zielezinski, A., Vinga, S., Almeida, J., and Karlowski, W.M.. Alignment-free sequence comparison: benefits, applications, and tools. Genome Biology, 18:186, 2017.CrossRefGoogle ScholarPubMed

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  • References
  • Reinhard Diestel, Universität Hamburg
  • Book: Tangles
  • Online publication: 16 May 2024
  • Chapter DOI: https://doi.org/10.1017/9781009473323.021
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Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Reinhard Diestel, Universität Hamburg
  • Book: Tangles
  • Online publication: 16 May 2024
  • Chapter DOI: https://doi.org/10.1017/9781009473323.021
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Reinhard Diestel, Universität Hamburg
  • Book: Tangles
  • Online publication: 16 May 2024
  • Chapter DOI: https://doi.org/10.1017/9781009473323.021
Available formats
×