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Tangles and Connectivity in Graphs

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arxiv 1602.04727 v1 pith:5IVN4DGZ submitted 2016-02-15 cs.DM math.CO

Martin Grohe This is my paper · ORCID
classification cs.DMmath.CO
keywords tanglescomponentsconnectivitycorrespondencegraphsorderemphasisgeneral
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This paper is a short introduction to the theory of tangles, both in graphs and general connectivity systems. An emphasis is put on the correspondence between tangles of order k and k-connected components. In particular, we prove that there is a one-to-one correspondence between the triconnected components of a graph and its tangles of order 3.

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  1. On vertex sets inducing tangles

    math.CO 2024-11 conditional novelty 7.0 of 10

    Every k-tangle in a graph is the lift of a k-tangle in a topological minor of size bounded by a function of k, reducing the vertex-set induction problem to bounded-size graphs.

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