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Completely Independent Spanning Trees in Maximal Planar Graphs

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Graph-Theoretic Concepts in Computer Science (WG 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2573))

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Abstract

Let G be a graph. Let T 1, T 2, . . . , T k be spanning trees in G. If for any two vertices u, v in G, the paths from u to v in T 1, T 2, . . . , Tk are pairwise openly disjoint, then we say that T 1, T 2, . . . , Tk are completely independent spanning trees in G. In this paper, we show that there are two completely independent spanning trees in any 4-connected maximal planar graph. Our proof induces a linear-time algorithm for finding such trees. Besides, we show that given a graph G, the problem of deciding whether there exist two completely independent spanning trees in G is NP-complete.

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Author information

Authors and Affiliations

  1. Department of Computer Science, The University of Electro-Communications, 1-5-1 Chofugaoka, 182-8585, Chofu, Tokyo, Japan

    Toru Hasunuma

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  1. Toru Hasunuma
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Editor information

Editors and Affiliations

  1. Karlsruhe University, Germany

    Gerhard Goos

  2. Cornell University, NY, USA

    Juris Hartmanis

  3. Utrecht University, The Netherlands

    Jan van Leeuwen

  4. Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00, Prague, Czech Republic

    Luděk Kučera

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© 2002 Springer-Verlag Berlin Heidelberg

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Hasunuma, T. (2002). Completely Independent Spanning Trees in Maximal Planar Graphs. In: Goos, G., Hartmanis, J., van Leeuwen, J., Kučera, L. (eds) Graph-Theoretic Concepts in Computer Science. WG 2002. Lecture Notes in Computer Science, vol 2573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36379-3_21

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  • DOI: https://doi.org/10.1007/3-540-36379-3_21

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00331-1

  • Online ISBN: 978-3-540-36379-8

  • eBook Packages: Springer Book Archive

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