Neuwirth manifolds and colourings of graphs (Q1207284)

Let \(M\) be a prime, orientable, connected, closed 3-manifold. A construction is described associating to certain Heegaard diagrams of \(M\) coloured graphs one of which represents \(M\) in the sense that the realisation of a simplicial complex obtained from the graph is homeomorphic to \(M\). These graphs are then used to classify a family of manifolds introduced by \textit{L. Neuwirth} [``An algorithm for the construction 3-manifolds from 2-complexes'', Proc. Camb. Philos. Soc. 64, 603-613 (1968; Zbl 0162.276)] as Seifert fibred spaces.