  J.H.C. Whitehead's second free-group algorithm determines whether or not two
given elements of a free group lie in the same orbit of the automorphism group
of the free group. The algorithm involves certain connected graphs, and
Whitehead used three-manifold models to prove their connectedness; later,
Rapaport and Higgins & Lyndon gave group-theoretic proofs. Combined work of
Gersten, Stallings, and Hoare showed that the three-manifold models may be
viewed as graphs. We give the direct translation of Whitehead's topological
argument into the language of graph theory.
