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(t, s)-Completely Independent Spanning Trees

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WALCOM: Algorithms and Computation (WALCOM 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14549))

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Abstract

In this paper we first define (t, s)-completely independent spanning trees, which is a generalization of completely independent spanning trees. A set of t spanning trees of a graph is (t, s)-completely independent if, for any pair of vertices u and v, among the set of t paths from u to v in the t spanning trees, at least \(s\le t\) paths are internally disjoint. By (t, s)-completely independent spanning trees, one can ensure any pair of vertices can communicate each other even if at most \(s-1\) vertices break down. We prove that every maximal planar graph has a set of (3, 2)-completely independent spanning trees, every tri-connected planar graph has a set of (3, 2)-completely independent spanning trees, and every 3D grid graph has a set of (3, 2)-completely independent spanning trees. Also one can compute them in linear time.

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Authors and Affiliations

  1. Gunma University, Kiryu, 376-8515, Japan

    Shin-ichi Nakano

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  1. Shin-ichi Nakano
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Correspondence to Shin-ichi Nakano .

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Editors and Affiliations

  1. Japan Advanced Institute of Science and Technology, Nomi, Japan

    Ryuhei Uehara

  2. Iwate University, Morioka, Japan

    Katsuhisa Yamanaka

  3. National Taiwan University, Taipei, Taiwan

    Hsu-Chun Yen

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© 2024 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

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Nakano, Si. (2024). (t, s)-Completely Independent Spanning Trees. In: Uehara, R., Yamanaka, K., Yen, HC. (eds) WALCOM: Algorithms and Computation. WALCOM 2024. Lecture Notes in Computer Science, vol 14549. Springer, Singapore. https://doi.org/10.1007/978-981-97-0566-5_26

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  • DOI: https://doi.org/10.1007/978-981-97-0566-5_26

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-97-0565-8

  • Online ISBN: 978-981-97-0566-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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