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Minimally 3-connected isotropic systems

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Abstract

Isotropic systems are structures which unify some properties of 4-regular graphs and selfdual properties of binary matroids, such as connectivity and minors. In this paper, we find the minimally 3-connected isotropic systems. This result implies the binary part Tutte's wheels and whirls theorem.

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References

  1. L. Allys: 3-connexité dans les systèmes isotropes, Thèse, Université du Maine (1992).

  2. A. Bouchet: Reducing prime graphs and recognizing circle graphs,Combinatorica 7 (1987), 243–254.

    Google Scholar 

  3. A. Bouchet: Isotropic systems,European J. of Combin. 8, (1987), 231–244.

    Google Scholar 

  4. A. Bouchet: Digraph decomposition and Eulerian systems,SIAM J. Alg. Disc. Meth. 8 (1987), 323–337.

    Google Scholar 

  5. A. Bouchet: Graphic representations of isotropic systems,J. Combinatorial Theory B 45 (1988), 58–76.

    Google Scholar 

  6. A. Bouchet: Connectivity of isotropic systems,Annals of the New York Academy of Sciences 555 (1989), 81–93.

    Google Scholar 

  7. W. Cunningham andJ. Edmonds: A combinatorial decomposition theory,Canad. J. Math. XXXII (1982), 734–765.

    Google Scholar 

  8. W. Cunningham: Decomposition of directed graphs,SIAM J. Alg. Disc. Meth. 3 (1987), 214–218.

    Google Scholar 

  9. W. Tutte: Connectivity in matroids,Canad. J. Math. 18 (1966), 1301–1324.

    Google Scholar 

  10. D. J. A. Welsh: Matroid Theory,London Math. Soc. Monographs,8, Academic Press, New York, 1976.

    Google Scholar 

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Allys, L. Minimally 3-connected isotropic systems. Combinatorica 14, 247–262 (1994). https://doi.org/10.1007/BF01212973

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  • DOI: https://doi.org/10.1007/BF01212973

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