A nonorientable triangular embedding of \(K_ n-K_ 2\), \(n\equiv 8\pmod{12}\)
It was known that a nonorientable triangular embedding of \(K_8- K_2\) does not exist. Whether there exists a nonorientable triangular embedding of \(K_{12s+ 8}- K_2\), \(s\geq 1\), remained open. In this paper, the author constructs such an embedding and thus gives an affirmative answer to this open question. The technique employed to construct the embedding is a special case of the general method of index 2 current graphs for producing triangular embeddings of the graphs \(K_{2n+ m}- K_m\) proposed by the author earlier, where \(m\) may increase indefinitely as \(n\) increases.
scientific article; zbMATH DE number 778536