Extremal graph theory for metric dimension and diameter.
Hernando, Carmen, Mora, Mercè, Pelayo, Ignacio M., Seara, Carlos, Wood, David R. (2010)
The Electronic Journal of Combinatorics [electronic only]
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Extremal graph theory for metric dimension and diameter.
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Let X be a connected graph with uniformly bounded degree. We show that if there is a radius r such that, by removing from X any ball of radius r, we get at least three unbounded connected components, then X satisfies a strong isoperimetric inequality. In particular, the non-reduced -cohomology of X coincides with the reduced -cohomology of X and is of uncountable dimension. (Those facts are well known when X is the Cayley graph of a finitely generated group with infinitely many ends.) ...
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