Grannell, M.J. and Korzhik, V.P.
Nonorientable biembeddings of Steiner triple systems.
Discrete Mathematics, 285(1-3),
Constructions due to Ringel show that there exists a nonorientable face 2-colourable triangular embedding of the complete graph on n vertices (equivalently a nonorientable biembedding of two Steiner triple systems of order n) for all n≡3 (mod 6) with n9. We prove the corresponding existence theorem for n≡1 (mod 6) with n13.
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