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Face two-colourable triangulations of \(K_{13}\). (English) Zbl 1036.05012

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 \(n=13\).

MSC:

05B07 Triple systems
05C10 Planar graphs; geometric and topological aspects of graph theory
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