EQUIVALENCE OF THE STRENGTHENED HANNA-NEUMANN CONJECTURE AND THE AMALGAMATED GRAPH CONJECTURE

We show that Walter Neumann's strengthened form of Hanna Neumann's con jecture on the best possible upper bound for the rank of the intersect ion of two subgroups of a free group is equivalent to a conjecture on the best possible upper bound for the number of edges in a bipartite g raph with a certain weak symmetry condition. We illustrate the usefuln ess of this equivalence by deriving relatively easily certain previous ly known results.