Nonrevisiting cycles on surfaces
A nonrevisiting cycle is a nonplanar cycle, in a polyhedral map \(M\), whose intersection with each face of \(M\) is either connected or empty. \textit{D. W. Barnette} [Discrete Math. 70, No. 1, 1-16 (1988; Zbl 0654.05024)] showed that the torus \(S_1\), the projective plane \(N_1\), and the Klein bottle \(N_2\) have such cycles. The present author uses a polygonal representation of a polyhedral map to extend Barnette's results to a class of polyhedral maps on \(S_2\) and \(N_3\).
scientific article; zbMATH DE number 1382642