Separating and nonseparating disjoint homotopic cycles in graph embeddings

Abstract

We show that if a graph G is embedded in a surface ∑ with representativity ρ, then G contains at least ⌊(ρ - 1)/2⌋ pairwise disjoint, pairwise homotopic, non-separating (in ∑) cycles, and G contains at least ⌊(ρ - 1)/8⌋ - 1 pairwise disjoint, pairwise homotopic, separating, noncontractible cycles. © 1996 Academic Press, Inc.