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An Extension of a Theorem of Henneberg and Laman

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Integer Programming and Combinatorial Optimization (IPCO 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2081))

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Abstract

We give a constructive characterization of graphs which are the union of k spanning trees after adding any new edge. This is a generalization of a theorem of Henneberg and Laman who gave the characterization for k = 2.

We also give a constructive characterization of graphs which have k edge-disjoint spanning trees after deleting any edge of them.

Research supported by the Hungarian National Foundation for Scientific Research Grant, OTKA T17580.

This author is supported by the Siemens-ZIB Fellowship Program and FKFP grant no. 0143/2001.

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Author information

Authors and Affiliations

  1. Department of Operations Research, Eötvös University, Kecskeméti u. 10-12, Budapest, Hungary, H-1053

    András Frank

  2. Ericsson Traffic Laboratory, Laborc u. 1, Budapest, Hungary, H-1037

    András Frank & László Szegő

Authors
  1. András Frank
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  2. László Szegő
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Editor information

Editors and Affiliations

  1. Instituut voor Informatica en Informatiekunde, Universiteit Utrecht, Padualaan 14, 3584, CH Utrecht, The Netherlands

    Karen Aardal

  2. CWI, Kruislaan 413, 1098, SJ Amsterdam, The Netherlands

    Bert Gerards

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© 2001 Springer-Verlag Berlin Heidelberg

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Frank, A., Szegő, L. (2001). An Extension of a Theorem of Henneberg and Laman. In: Aardal, K., Gerards, B. (eds) Integer Programming and Combinatorial Optimization. IPCO 2001. Lecture Notes in Computer Science, vol 2081. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45535-3_12

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  • DOI: https://doi.org/10.1007/3-540-45535-3_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42225-9

  • Online ISBN: 978-3-540-45535-6

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