Highly linked graphs

AbstractA graph with at least 2k vertices is said to bek-linked if, for any choices1,...,sk,t1,...,tkof 2k distinct vertices there are vertex disjoint pathsP1,...,PkwithPijoiningsitoti, 1≤i≤k. Recently Robertson and Seymour [16] showed that a graphG isk-linked provided its vertex connectivityk(G) exceeds $$10k\sqrt {\log _2 k}$$ . We show here thatk(G)≥22k will do.

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