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Geometric Graphs Realization as Coin Graphs

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Computational Science and Its Applications – ICCSA 2004 (ICCSA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3045))

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Abstract

Koebe’s Theorem [8] proves that any planar graph is the contact graph of a set of coins in the plane. But not any planar geometric graph can be realized as a coin graph (with coins centered at the vertices of the graph). This paper presents an algorithm to decide whether a planar connected geometric graph is a coin graph and to obtain, in the affirmative case, all the coin sets whose contact graphs are the given graph. This result is generalized to other metrics different from the Euclidean metric and is applied to a problem in mechanical gear systems. Two related optimization problems are also considered. They are motivated by graph drawing problems in Geographical Information Systems and Architectural Design Systems.

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References

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Authors and Affiliations

  1. Dpto. Mat. Aplic, FI. UPM., 28660, Boadilla del Monte, Madrid, Spain

    Manuel Abellanas & Carlos Moreno-Jiménez

Authors
  1. Manuel Abellanas
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  2. Carlos Moreno-Jiménez
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Editor information

Editors and Affiliations

  1. Department of Chemistry, University of Perugia, Via Elce di Sotto, 8, I-06123, Perugia, Italy

    Antonio Laganá

  2. Department of Computer Science, University of Calgary, 2500 University Drive N.W., T2N 1N4, Calgary, AB, Canada

    Marina L. Gavrilova

  3. William Norris Professor, Head of the Computer Science and Engineering Department, University of Minnesota, USA

    Vipin Kumar

  4. School of Computing, Soongsil University, Seoul, Korea

    Youngsong Mun

  5. OptimaNumerics Ltd., Cathedral House, 23-31 Waring Street, BT1 2DX, Belfast, UK

    C. J. Kenneth Tan

  6. Department of Mathematics and Computer Science, University of Perugia, via Vanvitelli, 1, I-06123, Perugia, Italy

    Osvaldo Gervasi

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© 2004 Springer-Verlag Berlin Heidelberg

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Abellanas, M., Moreno-Jiménez, C. (2004). Geometric Graphs Realization as Coin Graphs. In: Laganá, A., Gavrilova, M.L., Kumar, V., Mun, Y., Tan, C.J.K., Gervasi, O. (eds) Computational Science and Its Applications – ICCSA 2004. ICCSA 2004. Lecture Notes in Computer Science, vol 3045. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24767-8_1

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  • DOI: https://doi.org/10.1007/978-3-540-24767-8_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22057-2

  • Online ISBN: 978-3-540-24767-8

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