Geodesic
Tangles are Decided by Weighted Vertex Sets
Advances in Combinatorics (2020)
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We show that, given a $ k $-tangle $ τ$ in a graph $ G $, there always exists a weight function $ w\colon V(G)\to\mathbb{N} $ such that a separation $ (A,B) $ of $ G $ of order $ {}k $ lies in $ τ$ if and only if $ w(A)$, where $ w(U) := \sum_{u\in U}w(u) $ for $ U\subseteq V(G) $. We show that the same result holds also for tangles of hypergraphs as well as for edge-tangles of graphs, but not for edge-tangles of hypergraphs.
Publié le : 
@article{ADVC_2020_a2,
     author = {Christian Elbracht and Jay Lilian Kneip and Maximilian Teegen},
     title = {Tangles are {Decided} by {Weighted} {Vertex} {Sets}},
     journal = {Advances in Combinatorics},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADVC_2020_a2/}
}
TY  - JOUR
AU  - Christian Elbracht
AU  - Jay Lilian Kneip
AU  - Maximilian Teegen
TI  - Tangles are Decided by Weighted Vertex Sets
JO  - Advances in Combinatorics
PY  - 2020
UR  - http://geodesic.mathdoc.fr/item/ADVC_2020_a2/
LA  - en
ID  - ADVC_2020_a2
ER  - 
%0 Journal Article
%A Christian Elbracht
%A Jay Lilian Kneip
%A Maximilian Teegen
%T Tangles are Decided by Weighted Vertex Sets
%J Advances in Combinatorics
%D 2020
%U http://geodesic.mathdoc.fr/item/ADVC_2020_a2/
%G en
%F ADVC_2020_a2
Christian Elbracht; Jay Lilian Kneip; Maximilian Teegen. Tangles are Decided by Weighted Vertex Sets. Advances in Combinatorics (2020). http://geodesic.mathdoc.fr/item/ADVC_2020_a2/