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Reconstructing 1-coherent locally finite trees

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Commentarii Mathematici Helvetici

Abstract

We prove a theorem implying the conjecture of J. A. Bondy and R. L. Hemminger that an infinite, locally finite tree containing no two-way infinite path is uniquely determined, up to isomorphism, from its collection of vertex-deleted subgraphs.

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References

  1. J. A. Bondy andR. L. Hemminger,Reconstructing infinite graphs, Pacific J. Math.52 (1974), 331–340.

    MathSciNet  Google Scholar 

  2. -J. A. Bondy and -R. L. Hemminger,Almost reconstructing infinite graphs, in: Recent Advances in Graph Theory (Proc. of the Symposium held in Prague, 1974, M. Fiedler, ed.) Academia, Prague, 69–73.

  3. — and —,Problem in the Proceedings of the Fifth British Combinatorial Conference, Congressus Numeratium XV, C. St. J. A. Nash-Williams and J. Sheehan, Eds., Utilitas Mathematica Publishing Inc., Winnipeg, 1976, p. 696.

    Google Scholar 

  4. — and-—,Graph Reconstruction—A Survey, J. Graph Theory1 (1977), 227–268.

    MathSciNet  Google Scholar 

  5. J. Fisher R. L. Graham andF. Harary,A counterexample to the countable version of a conjecture of Ulam, J. Combinatorial Theory (B)12 (1972), 203–204.

    Article  MathSciNet  Google Scholar 

  6. F. Harary, A. J. Schwenk andR. L. Scott,On the reconstruction of countable forests, Publ. Math. Inst. (Beograd)13 (1972), 39–42.

    MathSciNet  Google Scholar 

  7. J. Neŝetřil,On reconstructing of infinite forests, Comment. Univ. Math. Carolinae13 (1972), 503–510.

    Google Scholar 

  8. J. Neŝetřil,On reconstruction of infinite forests II, Comment. Math. Univ. Carolinae, to appear.

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Thomassen, C. Reconstructing 1-coherent locally finite trees. Commentarii Mathematici Helvetici 53, 608–612 (1978). https://doi.org/10.1007/BF02566101

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  • DOI: https://doi.org/10.1007/BF02566101

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