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Tangles and the Mona Lisa

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arxiv 1603.06652 v3 pith:WLR7AJKW submitted 2016-03-22 math.CO cs.ITmath.IT

Reinhard Diestel , Geoff Whittle This is my paper · ORCID
classification math.COcs.ITmath.IT
keywords graphimagetanglestangletheoremcannotcertain-ordercontains
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We show how an image can, in principle, be described by the tangles of the graph of its pixels. The tangle-tree theorem provides a nested set of separations that efficiently distinguish all the distinguishable tangles in a graph. This translates to a small data set from which the image can be reconstructed. The tangle duality theorem says that a graph either has a certain-order tangle or a tree-structure witnessing that this cannot exist. This tells us the maximum resolution at which the image contains meaningful information.

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  1. Representations of infinite tree-sets

    math.CO 2019-08 conditional novelty 7.0 of 10

    Every regular infinite tree set is represented by the edge tree set of a tree-like space, and the regular tame ones are exactly the edge tree sets of ordinary trees.

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