Abstract
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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References
C. Berge,Graphs and hypergraphs, North Holland, Amsterdam, 1973.
R. G. Bland andM. Las Vergnas, Orientability of matroids,J. Combinatorial Theory, Ser. B 24 (1978), 94–123.
R.Cordovil and P.Duchet, On the number of signinvariant pairs of points in oriented matroids,preprint, 1984.
J. Folkman andJ. Lawrence, Oriented matroids,J. Combinatorial Theory, Ser. B 25 (1978), 199–236.
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.
B. Grünbaum,Convex polytopes, Wiley, Interscience, London, 1967.
H. A. Jung, Eine Verallgemeinerung desn-fachen Zusammenhangs für Graphen,Math. Ann. 187 (1970), 95–103.
M. Las Vergnas, Matroïdes orientables,C. R. Acad. Sci. Paris,280 (1975), 61–64.
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.
J. Lawrence andL. Weinberg, Unions of oriented matroids,Linear Algebra and Appl.,41 (1981), 183–200.
J. P.Raudneff, Reconstruction of the orientation class of an oriented matroid,Europ. J. Combinatorics.
P. D. Seymour, Disjoint paths in graphs,Discrete Math.,29 (1980), 293–309.
C. Thomassen, 2-linked graphs,Europ. J. Combinatorics 1 (1980), 371–378.
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Roudneff, J.P. Inseparability graphs of oriented matroids. Combinatorica 9, 75–84 (1989). https://doi.org/10.1007/BF02122686
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DOI: https://doi.org/10.1007/BF02122686