Completely strong path-connected tournaments

AbstractLet T = (V, A) be a tournament with p vertices. T is called completely strong path-connected if for each arc (a, b) ∈ A and k (k = 2, 3,…, p), there is a path from b to a of length k (denoted by Pk(a, b)) and a path from a to b of length k (denoted by P′k(a, b)). In this paper, we prove that T is completely strong path-connected if and only if for each arc (a, b) ∈ A, there exist P2(a, b), P′2(a, b) in T, and T satisfies one of the following conditions: (a) T/T0-type graph, (b) T is 2-connected, (c) for each arc (a, b) ∈ A, there exists a P′p−1(a, b) in T