Abstract
A digraph is k-linked if for any two disjoint sets of vertices {x1,…,xk} and {y1,…,yk} there are vertex disjoint paths P1,…,Pk such that Pi is directed from xi to yi for i=1,…,k. Pokrovskiy in 2015 proved that every strongly 452k-connected tournament is k-linked. In this paper, we significantly reduce this connectivity bound and show that any (40k−31)-connected tournament is k-linked.
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