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Structure trees, networks and almost invariant sets. (English) Zbl 1371.05045

Ceccherini-Silberstein, Tullio (ed.) et al., Groups, graphs and random walks. Selected papers of the workshop, Cortona, Italy, June 2–6, 2014 on the occasion of the 60th birthday of Wolfgang Woess. Cambridge: Cambridge University Press (ISBN 978-1-316-60440-3/pbk; 978-1-316-57657-1/ebook). London Mathematical Society Lecture Note Series 436, 137-175 (2017).
Summary: A self-contained account of the theory of structure trees for edge cuts in networks is given. Applications include a generalisation of the max-flow min-cut theorem to infinite networks and a short proof of a conjecture of P. H. Kropholler [Proc. Lond. Math. Soc., III. Ser. 60, No. 3, 503–529 (1990; Zbl 0704.20023)]. This gives a relative version of Stallings’ theorem on the structure of groups with more than one end. A generalisation of the almost stability theorem is also obtained, which provides information about the structure of the Sageev cubing.
For the entire collection see [Zbl 1370.05004].

MSC:

05C05 Trees
05C82 Small world graphs, complex networks (graph-theoretic aspects)
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
20F65 Geometric group theory

Citations:

Zbl 0704.20023
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