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5 - Structure Trees, Networks and Almost Invariant Sets

Published online by Cambridge University Press:  20 July 2017

Martin J. Dunwoody
University of Southampton, Southampton, United Kingdom
Tullio Ceccherini-Silberstein
Università degli Studi del Sannio, Italy
Maura Salvatori
Università degli Studi di Milano
Ecaterina Sava-Huss
Cornell University, New York
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Publisher: Cambridge University Press
Print publication year: 2017

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[1] Ian, Chiswell, Introduction to Ʌ-trees, World Scientific, 2001.
[2] Warren, Dicks, Group, trees and projective modules, Springer Lecture Notes 790 (1980).Google Scholar
[3] Warren, Dicks and M.J., Dunwoody, Groups acting on graphs, Cambridge University Press, 1989. Errata∼dicks/
[4] V., Diekert and A., Weiss, Context free groups and their structure trees, arXiv:1202.3276.
[5] E.A., Dinits, A.V., Karzanov and M.V., Lomonosov, On the structure of a family of minimal weighted cuts in a graph. Studies in Discrete Optimization [Russian], [290–306, Nanka, Moscow (1976).
[6] M.J., Dunwoody, Cutting up graphs, Combinatorica 2 (1982) 15–23.Google Scholar
[7] M.J., Dunwoody, Accessibility and groups of cohomological dimension one, Proc. London Math. Soc. 38 (1979) 193–215.Google Scholar
[8] M.J., Dunwoody, The accessibility of finitely presented group, Invent. Math. 81 (1985) 449–57. 193–215.Google Scholar
[9] M.J., Dunwoody, An inaccessible group, London Math. Soc. Lecture Note Series 181 (1991) 173–8.Google Scholar
[10] M.J., Dunwoody, Inaccessible groups and protrees, J. Pure Applied Al. 88 (1993) 63–78.Google Scholar
[11] M.J., Dunwoody, Planar graphs and covers, arXiv 193–215.
[12] M.J., Dunwoody, Structure trees and networks, arXiv:1311.3929.
[13] M.J., Dunwoody, Almost invariant sets, arXiv 1409–6782.
[14] M.J., Dunwoody and B., Krön,Vertex Cuts, J. Graph Theory (published on line 2014).
[15] M.J., Dunwoody and M., Roller, Splitting groups over polycyclic-by-finite subgroups, Bull. London Math. Soc. 23 (1989) 29–36.Google Scholar
[16] T., Fleiner and A., Frank, Aquick proof for the cactus representation of mincuts, EGRES Quick-Proof No. 2009–03.
[17] L.R., Ford, Jr. and D.R., Fulkerson, Maximal flow through a network, Canadian Journal of Mathematics 8 (1956) 399–404.Google Scholar
[18] R.E., Gomory and T. C., Hu Multi-terminal network flows. Journal of the Society for Industrial and Applied Mathematics, 9, (1961) 551–70.Google Scholar
[19] A., Evangelidou and P., Papasoglu, A cactus theorem for edge cuts, International J. of Algebra and Computation 24 (2014) 95–107.Google Scholar
[20] A., Kar and G.A., Niblo, Relative ends ℓ2-invariants and property T, arXiv:1003.2370.
[21] B., Krön, Cutting up graphs revisited, Groups Complex. Cryptol. 2 (2010) 213–21.Google Scholar
[22] P.H., Kropholler, An analogue of the torus decomposition theorem for certain Poincaré groups, Proc. London Math. Soc. (3) 60 (1990) 503–29.Google Scholar
[23] P.H., Kropholler, A group theoretic proof of the torus theorem, London Math. Soc. Lecture Note Series 181 (1991) 138–58.Google Scholar
[24] H.D., Macpherson, Infinite distance transitive graphs of finite valency Combinatorica 2 (1982) 62–9.Google Scholar
[25] R.G., Möller, Ends of graphs, Math. Proc. Camb. Phil. Soc 111 (1992) 255–66.Google Scholar
[26] G.A., Niblo, A geometric proof of Stallings theorem on groups with more than one end, Geometriae Dedicata 105, 61–76 (2004).Google Scholar
[27] R.B., Richter and C., Thamassen, 3-connected planar spaces uniquely embed in the sphere, Trans. Amer. Math. Soc. 354 (2002) 4585–95.Google Scholar
[28] G., Niblo and M., Sageev, The Kropholler conjecture. In Guido's Book of Conjectures, Monographies de L'Enseignement Mathématique, 40. L'Enseignement Mathématique, Geneva, 2008.
[29] M., Sageev, Ends of group pairs and non-positively curved cube complexes, Proc. London Math. Soc. (3) 71 (1995) 585–617.Google Scholar
[30] J.-P., Serre, Trees. Translated from the French by John, Stillwell. Springer- Verlag, Berlin-New York, 1980.
[31] J.R., Stallings, Group theory and three-dimensional manifolds. Yale Mathematical Monographs, 4. Yale University Press, New Haven, Conn.- London, 1971.
[32] C., Thomassen and W., Woess, Vertex-transitive graphs and accessibility, J. Combin. Theory Ser. B 58 (1993) 248–68.Google Scholar
[33] W.T., Tutte, Graph Theory. Cambridge University Press, 1984.
[34] C.T.C., Wall. Pairs of relative cohomological dimension one, J. Pure Appl. Algebra 1 (1971) 141–54.Google Scholar
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