Seifert unions and spaces of graphs in **S ^{3}**

J. C. Gomez-Larranaga, W. Heil

Let Gamma be a non-splittable graph in S^3, not a tree. It is shown that if the space M=\overline{S^3-N(Gamma)} of Gamma is a Seifert union of solid tori then M is homeomorphic to the space of a tree of Burde-Murasugi links.