Grannell, M. J.; Griggs, T. S.; Knor, M. Face two-colourable triangulations of \(K_{13}\). (English) Zbl 1036.05012 J. Comb. Math. Comb. Comput. 47, 75-81 (2003). It is well known that a face two-colorable embedding of the complete graph \(K_{n}\) may exist only if \(n\equiv 1, 3 \pmod6.\) It is easy to see that each color class of such embeddings forms a Steiner triple system of order \(n\). In the paper, these embeddings are constructed for \(n=13\). Reviewer: Peter Horák (Tacoma) Cited in 1 Document MSC: 05B07 Triple systems 05C10 Planar graphs; geometric and topological aspects of graph theory Keywords:Steiner triple system; embedding PDFBibTeX XMLCite \textit{M. J. Grannell} et al., J. Comb. Math. Comb. Comput. 47, 75--81 (2003; Zbl 1036.05012)