The first diameter of 3-manifolds of positive scalar curvature

We seek a universal upper bound for the first diameter of 3 3 -manifolds of scalar curvature ≥<!-- ≥ --> + 1 ≥ + 1 . We find it in the case of finite fundamental group by using a combinatorial theorem about finite trees, and in the case when π<!-- π --> 1 {π _1} is infinite cyclic by using a weak notion of a π<!-- π --> 1 {π _1} -equivariant Busemann function.