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Transactions of the American Mathematical Society

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On graphs with a metric end space

Author: Kerstin Waas
Journal: Trans. Amer. Math. Soc. 351 (1999), 1043-1062
MSC (1991): Primary 05C10
MathSciNet review: 1487635
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Abstract: R. Diestel conjectured that an infinite graph contains a topologically end-faithful forest if and only if its end space is metrizable. We prove this conjecture for uniform end spaces.

References [Enhancements On Off] (What's this?)

  • 1. J.-M. Brochet and R. Diestel, Normal tree orders for infinite graphs, Trans. Amer. Math. Soc. 345 (1994), no. 2, 871–895. MR 1260198, 10.1090/S0002-9947-1994-1260198-4
  • 2. Reinhard Diestel, The end structure of a graph: recent results and open problems, Discrete Math. 100 (1992), no. 1-3, 313–327. Special volume to mark the centennial of Julius Petersen’s “Die Theorie der regulären Graphs”, Part I. MR 1172358, 10.1016/0012-365X(92)90650-5
  • 3. Reinhard Diestel, On spanning trees and 𝑘-connectedness in infinite graphs, J. Combin. Theory Ser. B 56 (1992), no. 2, 263–277. MR 1186759, 10.1016/0095-8956(92)90022-P
  • 4. R. Halin, Über unendliche Wege in Graphen, Math. Ann. 157 (1964), 125–137 (German). MR 0170340
  • 5. R. Halin, Simplicial decompositions of infinite graphs, Ann. Discrete Math. 3 (1978), 93–109. Advances in graph theory (Cambridge Combinatorial Conf., Trinity Coll., Cambridge, 1977). MR 499113
  • 6. Rudolf Halin, Graphentheorie. I, Erträge der Forschung [Research Results], vol. 138, Wissenschaftliche Buchgesellschaft, Darmstadt, 1980 (German). MR 586234
    Rudolf Halin, Graphentheorie. II, Erträge der Forschung [Research Results], vol. 161, Wissenschaftliche Buchgesellschaft, Darmstadt, 1981 (German). MR 668698
  • 7. I. M. James, Topological and uniform spaces, Undergraduate Texts in Mathematics, Springer-Verlag, New York, 1987. MR 884154
  • 8. H. A. Jung, Wurzelbäume und unendliche Wege in Graphen, Math. Nachr. 41 (1969), 1–22 (German). MR 0266807
  • 9. Dénes König, Theorie der endlichen und unendlichen Graphen. Kombinatorische Topologie der Streckenkomplexe, Chelsea Publishing Co., New York, N. Y., 1950 (German). MR 0036989
  • 10. Horst Schubert, Topologie. Eine Einführung, Mathematische Leitfäden, B. G. Teubner Verlagsgesellschaft, Stuttgart, 1964 (German). MR 0170313
  • 11. P.D. Seymour and R. Thomas, An end-faithful counterexample. Directions in Infinite Graph Theory and Combinatorics (R. Diestel, Ed.), Topics in Discrete Mathematics 3, North-Holland Publ. Co., Amsterdam / London, 1992. CMP 92:14
  • 12. C. Thomassen, Infinitely connected graphs with no end-preserving spanning trees. preprint, 1990.
  • 13. K. Waas, Topologisch endentreue Bäume in unendlichen Graphen. Diplomarbeit, Universität Bielefeld, 1994.

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Additional Information

Kerstin Waas
Affiliation: Fakultät für Mathematik, TU Chemnitz D-09107 Chemnitz, Germany

Keywords: Infinite graph, topological end space, uniformly end-faithful, topologically end-faithful
Received by editor(s): January 20, 1997
Additional Notes: Supported by Deutsche Forschungsgemeinschaft
Article copyright: © Copyright 1999 American Mathematical Society