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Tangle and Maximal Ideal

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10167))

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Abstract

Tangle is a dual notion of the graph parameter branch-width. The notion of tangle can be extended to connectivity systems. Ideal is an important notion that plays a foundational role in ring, set, and order theories. Tangle and (maximal) ideal are defined by axiomatic systems, and they have some axioms in common. In this paper, we define ideals on connectivity systems. Then, we address the relations between tangles and maximal ideals on connectivity systems. We demonstrate that a tangle can be considered as a non-principle maximal ideal on a connectivity system.

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Acknowledgements

This work was supported by JSPS KAKENHI Grant Number 15K00007.

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Authors and Affiliations

  1. Faculty of Science and Technology, Gunma University, 1-5-1 Tenjin-cho, Kiryu, Gunma, Japan

    Koichi Yamazaki

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  1. Koichi Yamazaki
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Correspondence to Koichi Yamazaki .

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Editors and Affiliations

  1. Universiti Teknologi Brunei, Bandar Seri Begawan, Brunei Darussalam

    Sheung-Hung Poon

  2. Bangladesh University of Engineering and Technology, Dhaka, Bangladesh

    Md. Saidur Rahman

  3. National Taiwan University, Taipei, Taiwan

    Hsu-Chun Yen

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Yamazaki, K. (2017). Tangle and Maximal Ideal. In: Poon, SH., Rahman, M., Yen, HC. (eds) WALCOM: Algorithms and Computation. WALCOM 2017. Lecture Notes in Computer Science(), vol 10167. Springer, Cham. https://doi.org/10.1007/978-3-319-53925-6_7

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  • DOI: https://doi.org/10.1007/978-3-319-53925-6_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-53924-9

  • Online ISBN: 978-3-319-53925-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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