曲面上图的偏斜度、交叉数与欧拉界

Skewness, crossing number and Euler's bound for graphs on surfaces

Paul C. Kainen

备注：: 16 pages, 57 references

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AI总结：

本文研究曲面上连通图的偏斜度、交叉数与欧拉下界之间的不等式关系，综述相关进展，并确定折叠立方体的亏格等新结果。

摘要：

对于每个连通图$G$和曲面$S$，我们考察著名的不等式串$δ_S(G) \leq μ_S(G) \leq ν_S(G)$，其中$μ$和$ν$分别表示偏斜度和交叉数，而$δ$是欧拉公式下界。文中综述了最新进展，并给出了关于“折叠”立方体的新结果，包括其亏格。

英文摘要：

For every connected graph $G$ and surface $S$, we consider the well-known string of inequalities $δ_S(G) \leq μ_S(G) \leq ν_S(G)$, where $μ$ and $ν$ denote skewness and crossing number and $δ$ is the Euler-formula lower bound. Recent developments are surveyed; new results are given for the ``folded'' cube including its genus.

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