Separating and nonseparating disjoint homotopic cycles in graph embeddings
We show that if a graph \(G\) is embedded in a surface \(\Sigma\) with representativity \(\rho\), then \(G\) contains at least \(\lfloor(\rho- 1)/2\rfloor\) pairwise disjoint, pairwise homotopic, nonseparating (in \(\Sigma\)) cycles, and \(G\) contains at least \(\lfloor(\rho- 1)/8\rfloor- 1\) pairwise disjoint, pairwise homotopic, separating, noncontractible cycles.
scientific article; zbMATH DE number 934789