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Graphs and Combinatorics pp 226–235Cite as

Reconstructing combinatorial geometries

  • Part III: Contributed Papers New Results On Graphs And Combinatorics
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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 406))

Abstract

Ulam-type reconstruction problems are given for combinatorial geometries. In particular the subgeometry generating function is evaluated from the subgeometry generating functions of single element deletions. This result is applied to graphs to give the chromatic polynomial (for vertices or regions) and a number of other invariants which can be computed from the deck of edge deletions.

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References

  1. Brylawski, T. H., A Decomposition for Combinatorial Geometries, Trans. Amer. Math. Soc. 171 (1972), 235–282.

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  3. Greenwell, D. L., and Hemminger, R. L., Reconstructing Graphs, The Many Facets of Graph Theory, Springer-Verlag, Berlin (1969), 91–114.

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  4. Harary, F., A Seminar on Graph Theory, Holt, Rinehart, and Winston, New York, New York, 1967.

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  5. Harary, F., and Welsh, D. J. A., Matroids Versus Graphs, The Many Facets of Graph Theory, Springer-Verlag, Berlin (1969), 155–170.

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  6. Stanley, R., Acyclic Orientation of Graphs, (to appear).

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  7. Tutte, W. T., Lectures on Matroids, J. Res. Nat. Bur. Stand. 69B(1965), 1–48.

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  9. Whitney, H., 2-isomorphic Graphs, Amer. J. Math. 55 (1933), 245–254.

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Author information

Authors and Affiliations

  1. University of North Carolina, USA

    Thomas H. Brylawski

Authors
  1. Thomas H. Brylawski
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Ruth A. Bari Frank Harary

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© 1974 Springer-Verlag Berlin

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Brylawski, T.H. (1974). Reconstructing combinatorial geometries. In: Bari, R.A., Harary, F. (eds) Graphs and Combinatorics. Lecture Notes in Mathematics, vol 406. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066444

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  • DOI: https://doi.org/10.1007/BFb0066444

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06854-9

  • Online ISBN: 978-3-540-37809-9

  • eBook Packages: Springer Book Archive

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