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Selected Topics in Operations Research and Mathematical Economics pp 325–335Cite as

On Two Problems Related to the Traveling Salesman Problem on Halin Graphs

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Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 226))

Abstract

It has been shown recently that the traveling salesman (TS) problem on Halin graphs can be solved by a polynomial-time algorithm. The purpose of this paper is to discuss two problems which result from this special case of the TS problem. One of the problems is a special case of the set-partitioning ( SP ) problem in which a set family consists of the vertex sets of “interior faces” of a plane tree. The other problem is to cover the interior faces of a plane graph by a set of vertices which are face-independent.

Fellow of the Alexander von Humboldt-Stiftung; on leave from the Institute of Computer Science, University of Wrocław, ul. Przesmyckiego 20, 51151 Wrocław, Poland

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References

  1. A. Bondy and L. Lovász, Lengths of Cycles in Halin Graphs, Manuscript, May 1983.

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  2. G. Cornuéjols, D. Naddef, and W. Pulleyblank, The Traveling Salesman Problem in Graphs with 3-edge Cuts, CORE Discussion Paper No. 8212, Center for Oper. Res. and Econometrics, Universite Catholique de Louvain, March 1982.

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  3. F. Harary, Graph Theory, Addison Wesley, Reading Mass., 1969.

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  4. M. Skowrońska, Properties of Halin Graphs ( in Polish ), Chapter 2 in Ph.D. Dissertation, Copernicus University, Toruń, January 1983.

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  5. M. M. Sysło, An Efficient Cycle Vector Space Algorithm for Listing all Cycles of a Planar Graph, SIAM J. Comput. 10(1981), 797–808.

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  6. M. M. Sysło and A. Proskurowski, On Halin Graphs, in: M. Borowiecki, J. W. Kennedy, and M. M. Sysło, Graph Theory — Łagów 1981, LN in Mathematics, Springer-Verlag, Berlin-Heidelberg, 1983.

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Author information

Authors and Affiliations

  1. Institut für Ökonometrie und Operations Research, Universität Bonn, Nassestr. 2, D-5300, Bonn 1, Germany

    Maciej M. Sysło

Authors
  1. Maciej M. Sysło
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Editors and Affiliations

  1. Lehrstuhl für Anwendungen des Operations Research, Universität Karlsruhe, Kaiserstr. 12, D-7500, Karlsruhe 1, Germany

    Gerald Hammer

  2. Institut für Statistik und Mathematische Wirtschaftstheorie, Universität Karlsruhe, Kaiserstr. 12, D-7500, Karlsruhe 1, Germany

    Diethard Pallaschke

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© 1984 Springer-Verlag Berlin Heidelberg

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Sysło, M.M. (1984). On Two Problems Related to the Traveling Salesman Problem on Halin Graphs. In: Hammer, G., Pallaschke, D. (eds) Selected Topics in Operations Research and Mathematical Economics. Lecture Notes in Economics and Mathematical Systems, vol 226. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45567-4_25

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  • DOI: https://doi.org/10.1007/978-3-642-45567-4_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12918-9

  • Online ISBN: 978-3-642-45567-4

  • eBook Packages: Springer Book Archive

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