We show that if a graph G is embedded in a surface Sigma with representativity rho, then G contains at least right perpendicular(rho-1)/2left perpendicular pairwise disjoint, pairwise homotopic, nonseparating (in Sigma) cycles, and G contains at least right perpendicular(rho-1)/8left perpendicular-1 pairwise disjoint, pairwise homotopic, separating, noncontractible cycles. (C) 1996 Academic Press. Inc. [References: 16]
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机译：我们表明，如果绘图G嵌入具有代表性Rho的表面σ中，则G至少含有右垂直（RHO-1）/ 2LEFT垂直对成对，成对均单，非彼此（在SIGMA）循环中，并且G至少包含 右垂直（RHO-1）/ 8LEFT垂直-1对成对脱节，成对同型，分离，不可抵销的循环。 （c）1996年学术出版社。 Inc. [参考文献：16]
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