Graph Skeletons and Diminishing Minors
We introduce the notion of coarse bottlenecking in graphs and coarse skeletons of graphs and show how bottlenecking guarantees that a skeleton resembles (up to quasi-isometry) the original graph. We show how these tools can be used to simplify the structure of graphs upto quasi-isometry that have an...
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Zusammenfassung: | We introduce the notion of coarse bottlenecking in graphs and coarse
skeletons of graphs and show how bottlenecking guarantees that a skeleton
resembles (up to quasi-isometry) the original graph. We show how these tools
can be used to simplify the structure of graphs upto quasi-isometry that have
an excluded asymptotic minor, reducing it to a skeleton of the original
containing no $3$-fat minor. We give an example to show that a similar result
does not hold for $2$-fat minors. This makes progress towards a Conjecture
posed by Georgakopoulos and Papasoglu. |
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DOI: | 10.48550/arxiv.2405.17785 |