Inseparability graphs of oriented matroids


We determine the inseparability graphs of uniform oriented matroids and of graphic oriented matroids. For anyr, n such that 4≦r≦n−3, examples of rankr uniform oriented matroids onn elements with a given inseparability graph are obtained by simple constructions of polytopes having prescribed separation properties.

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  1. [1]

    C. Berge,Graphs and hypergraphs, North Holland, Amsterdam, 1973.

    Google Scholar 

  2. [2]

    R. G. Bland andM. Las Vergnas, Orientability of matroids,J. Combinatorial Theory, Ser. B 24 (1978), 94–123.

    Google Scholar 

  3. [3]

    R.Cordovil and P.Duchet, On the number of signinvariant pairs of points in oriented matroids,preprint, 1984.

  4. [4]

    J. Folkman andJ. Lawrence, Oriented matroids,J. Combinatorial Theory, Ser. B 25 (1978), 199–236.

    Google Scholar 

  5. [5]

    J. E. Goodman andR. Pollack, Proof of Grünbaum's conjecture on the stretchability of certain arrangements of pseudolines,J. Combinatorial Theory, Ser. A 29 (1980), 385–390.

    Google Scholar 

  6. [6]

    B. Grünbaum,Convex polytopes, Wiley, Interscience, London, 1967.

    Google Scholar 

  7. [7]

    H. A. Jung, Eine Verallgemeinerung desn-fachen Zusammenhangs für Graphen,Math. Ann. 187 (1970), 95–103.

    Article  Google Scholar 

  8. [8]

    M. Las Vergnas, Matroïdes orientables,C. R. Acad. Sci. Paris,280 (1975), 61–64.

    Google Scholar 

  9. [9]

    M.Las Vergnas, Extensions ponctuelles d'une géométrie orientée,Problèmes combinatoires et théorie des graphes, Proc. Coll. Orsay (1976), Editions du C.N.R.S.

  10. [10]

    J. Lawrence andL. Weinberg, Unions of oriented matroids,Linear Algebra and Appl.,41 (1981), 183–200.

    Article  Google Scholar 

  11. [11]

    J. P.Raudneff, Reconstruction of the orientation class of an oriented matroid,Europ. J. Combinatorics.

  12. [12]

    P. D. Seymour, Disjoint paths in graphs,Discrete Math.,29 (1980), 293–309.

    Article  Google Scholar 

  13. [13]

    C. Thomassen, 2-linked graphs,Europ. J. Combinatorics 1 (1980), 371–378.

    Google Scholar 

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Roudneff, J.P. Inseparability graphs of oriented matroids. Combinatorica 9, 75–84 (1989).

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AMS subject classification (1980)

  • 05 B 35