Show that br g does not depend on the choice of vertex o

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1 .Show that br G does not depend on the choice of vertex o

2 .Show that if G′ is a subgraph of G, then br G′ ≤ br G

If G is non-amenable, then br G > 1 by this exercise combined with the result of Benjamini and Schramm (1997) mentioned at the end of Section 6.1. Our bound for trees, Proposition 13.3, can be extended to general graphs as follows, but it is not as good as the one obtained for trees. See Section 13.8 for a better result.

Reference no: EM131267195

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