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Amenable group actions on infinite graphs

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  1. Adyan, S.I.: Random walks on free periodic groups. Math. USSR Izv.21, 425–434 (1983)

    Google Scholar 

  2. Banach, S.: Sur le problème de la mesure. Fundam. Math.4, 7–33 (1923)

    Google Scholar 

  3. Dunwoody, M.J.: Cutting up graphs. Combinatorica2, 15–23 (1982)

    Google Scholar 

  4. Eymard, P.: Moyennes invariantes et représentations unitaires (Lecture Notes Mathematics, Vol. 300). Berlin Heidelberg New York: Springer 1972

    Google Scholar 

  5. Freudenthal, H.: Über die Enden diskreter Räume und Gruppen. Comment. Math. Helv.17, 1–38 (1944)

    Google Scholar 

  6. Grigrochuk, R.I.: Degrees of growth of finitely generated groups, and the theory of invariant means. Math. USSR Izv25, 259–300 (1985)

    Google Scholar 

  7. Halin, R.: Über unendliche Wege in Graphen. Math. Ann.157, 125–137 (1964)

    Article  Google Scholar 

  8. Halin, R.: Die Maximalzahl zweiseitig unendlicher Wege in Graphen. Math. Nachr.44, 119–127 (1970)

    Google Scholar 

  9. Halin, R.: Automorphisms and endomorphisms of infinite locally finite graphs. Abh. Math. Sem. Univ. Hamb.39, 251–283 (1973)

    Google Scholar 

  10. De la Harpe, P., Skandalis, G.: Un résultat de Tarski sur les actions moyennables de groupes et les partitions paradoxales. Enseign. Math., II Sér.32, 121–138 (1986)

    Google Scholar 

  11. Jung, H.A.: Connectivity in infinite graphs. In: Studies in Pure Math., pp. 137–143. L. Mirsky (ed). New York London: Academic Press 1971

    Google Scholar 

  12. Jung, H.A.: A note on fragments of infinite graphs. Combinatorica1, 285–288 (1981)

    Google Scholar 

  13. Ore, O.: Theory of graphs. Providence: Amer. Math. Soc. 1962

    Google Scholar 

  14. Nebbia, C.: On the amenability and the Kunze-Stein property for groups acting on a tree. Pac. J. Math. (to appear)

  15. Picardello, M.A., Woess, W.: Harmonic functions and ends of graphs. Proc. Edin. Math. Soc.31, 457–461 (1988)

    Google Scholar 

  16. Pier, J.P.: Amenable locally compact groups. New York: Wiley 1984

    Google Scholar 

  17. Soardi, P.M., Woess, W.: Amenability, unimodularity, and the spectral radius of random walks on infinite graphs. Preprint, Univ. Milano 1988

  18. Soardi, P.M., Woess, W.: Uniqueness of currents in infinite resistive networks. Discrete Appl. Math. (to appear)

  19. Stallings, J.: Group theory and three-dimensional manifolds. New Haven: Yale Univ. Press 1971

    Google Scholar 

  20. Tits, J.: Sur le groupe des automorphismes d'un arbre. In: Essays on topology and related topics, mémoires dédiés a G. de Rham, pp. 188–211. Berlin Heidelberg New York: Springer 1970

    Google Scholar 

  21. Tits, J.: A “theorem of Lie-Kolchin” for trees. In: Contributions to algebra, a collection of papers dedicated to Ellis Kolchin, pp. 377–388. New York London: Academic Press 1977

    Google Scholar 

  22. Trofimov, V.I.: Automorphism groups of graphs as topological objects. Math. Notes38, 717–720 (1985)

    Google Scholar 

  23. Von Neumann, J.: Zur allgemeinen Theorie des Maßes. Fund. Math.13, 73–116 (1929)

    Google Scholar 

  24. Wagon, S.: The Banach-Tarski paradox. Encyclopedia of Math.24. Cambridge: Cambridge Univ. Press 1985

    Google Scholar 

  25. Woess, W.: Graphs and groups with tree-like properties. J. Combin. Th., Ser. B (to appear)

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Dedicated to Professor Gert Sabidussi on the occasion of his sixtieth birthday

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Woess, W. Amenable group actions on infinite graphs. Math. Ann. 284, 251–265 (1989).

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