How can sparse graph theory be extended to large networks, where algorithms whose running time is estimated using the number of vertices are not good enough? I address this question by introducing ‘Local Separators’ of graphs. Applications include:

1.

A unique decomposition theorem for graphs along their local 2-separators analogous to the 2-separator theorem;

2.

an exact characterisation of graphs with no bounded subdivision of a wheel [9].

中文翻译：

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本地 2 分隔符

稀疏图论如何扩展到大型网络，其中使用顶点数估计运行时间的算法不够好？我通过引入图表的“局部分隔符”来解决这个问题。应用包括：

1.

沿局部 2-分隔符的图的独特分解定理，类似于 2-分隔符定理；

2.

图的精确表征，没有轮子的有界细分[9]。