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An Orientation Theorem with Parity Conditions

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Integer Programming and Combinatorial Optimization (IPCO 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1610))

Abstract

Given a graph G = (V, E) and a set \( T \subseteq V\), an orientation of G is called T-odd if precisely the vertices of T get odd in-degree. We give a good characterization for the existence of a T-odd orientation for which there exist k edge-disjoint spanning arborescences rooted at a prespecified set of k roots. Our result implies Nash-Williams’ theorem on covering the edges of a graph by k forests and a (generalization of a) theorem due to Nebeský on upper embeddable graphs.

Supported by the Hungarian National Foundation for Scientific Research Grant OTKA T029772.

Supported in part by the Danish Natural Science Research Council, grant no. 28808.

Basic Research in Computer Science, Centre of the Danish National Research Foundation.

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References

  1. I. Anderson, Perfect matchings of a graph, J. Combin. Theory Ser. B, 10 (1971), 183–186.

    Article  MATH  Google Scholar 

  2. O. Chevalier, F. Jaeger, C. Payan and N.H. Xuong, Odd rooted orientations and upper-embeddable graphs, Annals of Discrete Mathematics 17, (1983) 177–181.

    MATH  MathSciNet  Google Scholar 

  3. J. Edmonds, Edge-disjoint branchings, in: R. Rustin (Ed.), Combinatorial Algorithms, Academic Press, (1973) 91–96.

    Google Scholar 

  4. A. Frank, Orientations of graphs and submodular flows, Congr. Numer. 113 (1996), 111–142.

    MATH  MathSciNet  Google Scholar 

  5. A. Frank, Z. Király, Parity constrained k-edge-connected orientations, Proc. Seventh Conference on Integer Programming and Combinatorial Optimization (IPCO), Graz, 1999. LNCS, Springer, this issue.

    Google Scholar 

  6. M.L. Furst, J.L. Gross, and L.A. McGeoch, Finding a maximum genus graph imbedding, J. of the ACM, Vol. 35, No. 3, July 1988, 523–534.

    Article  MathSciNet  Google Scholar 

  7. M. Jungerman, A characterization of upper embeddable graphs, Trans. Amer. Math. Soc. 241 (1978), 401–406.

    Article  MATH  MathSciNet  Google Scholar 

  8. C. St. J. A. Nash-Williams, Edge-disjoint spanning trees of finite graphs, J. London Math. Soc. 36 (1961), 445–450.

    Article  MATH  MathSciNet  Google Scholar 

  9. L. Nebeský, A new characterization of the maximum genus of a graph, Czechoslovak Mathematical Journal, 31(106) 1981, 604–613.

    Google Scholar 

  10. L. Lovász, Selecting independent lines from a family of lines in a space, Acta Sci. Univ. Szeged 42, 1980, 121–131.

    MATH  Google Scholar 

  11. N.H. Xuong, How to determine the maximum genus of a graph, J. Combin. Theory Ser. B 26 (1979), 217–225.

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Operations Research, Eötvös University, H-1088, Rákóczi út 5., Budapest, Hungary

    András Frank

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

    András Frank

  3. BRICS, Department of Computer Science, University of Aarhus, Ny Munkegade, building 540, DK-8000, Aarhus C, Denmark

    Tibor Jordán

  4. Equipe Combinatoire, Université Paris VI, 4, place Jussieu, 75252, Paris, France

    Zoltán Szigeti

Authors
  1. András Frank
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  2. Tibor Jordán
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  3. Zoltán Szigeti
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Editor information

Editors and Affiliations

  1. GSIA, Carnegie Mellon University, Schenley Park, Pittsburgh, PA, 15213, USA

    Gérard Cornuéjols

  2. Institut für Mathematik, Technische Universität Graz, Steyrergasse 30, A-8010, Graz, Austria

    Rainer E. Burkard  & Gerhard J. Woeginger  & 

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© 1999 Springer-Verlag Berlin Heidelberg

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Frank, A., Jordán, T., Szigeti, Z. (1999). An Orientation Theorem with Parity Conditions. In: Cornuéjols, G., Burkard, R.E., Woeginger, G.J. (eds) Integer Programming and Combinatorial Optimization. IPCO 1999. Lecture Notes in Computer Science, vol 1610. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48777-8_14

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  • DOI: https://doi.org/10.1007/3-540-48777-8_14

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66019-4

  • Online ISBN: 978-3-540-48777-7

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