  A matroid complex is a pure complex such that every restriction is again
pure. It is a long-standing open problem to classify all possible $h$-vectors
of such complexes. In the case when the complex has dimension 1 we completely
resolve this question. We also prove the 1-dimensional case of a conjecture of
Stanley that all matroid $h$-vectors are pure ${O}$-sequences. Finally, we
completely characterize the Stanley-Reisner ideals of 1-dimensional matroid
complexes.
