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- W2900747872 abstract "A $k$-connected set in an infinite graph, where $k > 0$ is an integer, is a set of vertices such that any two of its subsets of the same size $ell leq k$ can be connected by $ell$ disjoint paths in the whole graph. We characterise the existence of $k$-connected sets of arbitrary but fixed infinite cardinality via the existence of certain minors and topological minors. We also prove a duality theorem for the existence of such $k$-connected sets: if a graph contains no such $k$-connected set, then it has a tree-decomposition which, whenever it exists, precludes the existence of such a $k$-connected set." @default.
- W2900747872 created "2018-11-29" @default.
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- W2900747872 date "2018-11-15" @default.
- W2900747872 modified "2023-09-27" @default.
- W2900747872 title "Characterising $k$-connected sets in infinite graphs" @default.
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