On the intersection of subgroups of a free group

SummaryThe Hanna Neumann Conjecture says that the intersection of subgroups of rankn+1 andm+1 of a free group has rank at mostnm+1. This paper proves the conjecture for the casem=1. (See Theorem 1.) Our methods imply that the strengthened Hanna Neumann Conjecture is also true in this case (Theorem 2′).