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On end-faithful spanning trees in infinite graphs

Published online by Cambridge University Press:  24 October 2008

Reinhard Diestel
Reinhard Diestel
Affiliation:
St John's College, Cambridge
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Extract

Let G be an infinite connected graph. A ray (from ν) in G is a 1-way infinite path in G (with initial vertex ν). An infinite connected subgraph of a ray R ⊂ G is called a tail of R. If X ⊂ G is finite, the infinite component of R\X will be called the tail of R in G\X.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 107 , Issue 3 , May 1990 , pp. 461 - 473
Copyright
Copyright © Cambridge Philosophical Society 1990

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References

REFERENCES

[1]Bollobás, B.. Graph Theory, an Introductory Course (Springer-Verlag, 1979).Google Scholar
[2]Diestel, R.. Graph Decompositions – a Study in Infinite Graph Theory (Oxford University Press, 1990).CrossRefGoogle Scholar
[3]Diestel, R.. The structure of TK a-free graphs. (Submitted.)Google Scholar
[4]Diestel, R. (editor). Directions in Infinite Graph Theory, Annals of Discrete Math, (in preparation).Google Scholar
[5]Halin, R.. Über unendliche Wege in Graphen. Math. Ann. 157 (1964), 125–137.CrossRefGoogle Scholar
[6]Halin, R.. Automorphisms and endomorphisms of infinite locally finite graphs. Abh. Math. Sem. Univ. Hamburg 39 (1973), 251–283.CrossRefGoogle Scholar
[7]Halin, R.. Simplicial decompositions of infinite graphs. In Advances in Graph Theory, Annals of Discrete Math. vol. 3 (North-Holland Publ. Co., 1978), pp. 93–109.CrossRefGoogle Scholar
[8]Jung, H. A.. Wurzelbäume und unendliche Wege in Graphen. Math. Nachr. 41 (1969), 1–22.CrossRefGoogle Scholar
[9]König, D.. Theorie der Endlichen und Unendlichen Graphen (1936, reprinted by Chelsea Publ. Co., 1950).Google Scholar
[10]Polat, N.. Topological aspects of infinite graphs. In Cycles and Rays, NATO Adv. Study Institute Ser. C (Kluwer Academic Publishers, 1990), pp. 197–220.CrossRefGoogle Scholar
[11]Polat, N.. Spanning trees of infinite graphs. (Preprint, 1989.)Google Scholar
[12]Seifter, N.. The action of nilpotent groups on infinite graphs. Monatsh. Math. 99 (1985), 323–333.CrossRefGoogle Scholar
[13]Seymour, P. D. and Thomas, R.. An end-faithful counterexample. (Preprint, 1989.)Google Scholar
[14]Watkins, M. E.. Infinite paths that contain only shortest paths. J. Combin. Theory Ser. B 41 (1986), 341–355.CrossRefGoogle Scholar