On Intersections of Finitely Generated Subgroups of Free Groups

and asked if the factor 2 can be dropped. If one translates her approach (which is a slight modification of Howson's) to graph-theoretic terms, it easily shows that the answer is often "yes"in fact, for most U the answer is "yes" for all V. According to Gersten [G], the above problem has come to be known as the "Haana Neumann Conjecture." Using ideas of immersions of graphs originating from Stallings ([St]), Gersten solved the problem in some special cases (his approach is close to the one of Howson and Hanna Neumann, but seems weaker in practice). I am grateful to Alan Reid for bringing Gersten's paper to my attention, and also to Peter Neumann for leading me to other literature. In particular, [I] gives the same graph-theoretical translation of Hanna Neumann 's proof 1, and [Ni] and [Se] use similar methods to prove Burns ' bound [B]: