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Combing a Linkage in an Annulus
[article]

2022
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arXiv
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pre-print

A linkage in a graph G of size k is a subgraph L of G whose connected components are k paths. The pattern of a linkage of size k is the set of k pairs formed by the endpoints of these paths. A consequence of the Unique Linkage Theorem is the following: there exists a function f:ℕ→ℕ such that if a plane graph G contains a sequence 𝒞 of at least f(k) nested cycles and a linkage of size at most k whose pattern vertices lay outside the outer cycle of 𝒞, then G contains a linkage with the same

arXiv:2207.04798v1
fatcat:arquew3onfcu5ff5ql7iicppwu