Pokrovskiy conjectured that there is a function f: ℕ → ℕ such that any 2k-strongly-connected tournament with minimum out and in-degree at least f(k) is k-linked. In this paper, we show that any (2k + 1)-strongly-connected tournament with minimum out-degree at least some polynomial in k is k-linked, thus resolving the conjecture up to the additive factor of 1 in the connectivity bound, but without the extra assumption that the minimum in-degree is large. Moreover, we show the condition on high minimum out-degree is necessary by constructing arbitrarily large tournaments that are (2.5k − 1)-strongly-connected tournaments but are not k-linked.

Pokrovskiy 推测有一个函数f : ℕ → ℕ 使得任何具有最小输出和输入度至少f ( k ) 的2 k强连接锦标赛是k连接的。在本文中，我们证明了任何具有最小出度的(2 k + 1)-强连接锦标赛，至少k 中的某个多项式是k连接的，从而解决了连接范围中直到加性因子为 1 的猜想，但没有额外假设最小入度很大。此外，我们通过构建任意大的锦标赛（2.5 k− 1)-强关联的锦标赛，但不是k关联的。