Geodesic
On the complexity of graph-manifolds
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 190-191

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We provide a new formula for an upper bound of the complexity of non-Seifert graph-manifolds obtained by gluing together two Seifert manifolds fibered over the disc with two exceptional fibers. This bound turns out to be sharp for many manifolds. 
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E. A. Fominykh; M. A. Ovchinnikov. On the complexity of graph-manifolds. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 190-191. http://geodesic.mathdoc.fr/item/SEMR_2005_2_a24/