Abstract
We prove the following results in this paper. Let T be a tournament of order $$n\ge 3$$ with vertex set V and arc set E, x a vertex of maximum out-degree and y a vertex of minimum out-degree of T. If $$yx\in E$$ then there exists a path of length i from x to y for any i with $$2\le i \le n-1$$ ; and if $$xy\in E$$ , then there exists a path of length i from x to y for any i with $$3\le i \le n-1$$ unless xy is exceptional. We also give a very short discussion to almost regular tournaments and prove a result of Jakobsen.
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