Abstract

We show that if a graph G is embedded in a surface Σ with representativity ρ , then G contains at least ⌊( ρ −1)/2⌋ pairwise disjoint, pairwise homotopic, nonseparating (in Σ ) cycles, and G contains at least ⌊( ρ −1)/8⌋−1 pairwise disjoint, pairwise homotopic, separating, noncontractible cycles.

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