Locally finite graphs with an excluded finite minor have the weak coarse Menger property with f depending only on k and g linear in r independent of k.
A coarse-geometry characterization of cacti
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We give a quasi-isometric characterization of cacti, which is similar to Manning's characterization of quasi-trees by the bottleneck property. We also give another quasi-isometric characterization of cacti using fat theta curves.
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Every connected graph has a tree-decomposition with bounded-diameter adhesion sets and coarsely inseparable bags, yielding a metric analogue of the block-cutvertex tree.
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Coarse Menger property of quasi-minor excluded graphs and length spaces
Locally finite graphs with an excluded finite minor have the weak coarse Menger property with f depending only on k and g linear in r independent of k.
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A coarse block-cutvertex tree-decomposition
Every connected graph has a tree-decomposition with bounded-diameter adhesion sets and coarsely inseparable bags, yielding a metric analogue of the block-cutvertex tree.