平面图的Weisfeiler-Leman维数最多为3

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2017-06-20 DOI:10.1145/3333003

Sandra Kiefer, I. Ponomarenko, Pascal Schweitzer

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引用次数: 54

摘要

证明了所有有限平面图类的Weisfeiler-Leman (WL)维数不超过3。特别地，每一个有限的平面图在一阶逻辑中是可定义的，最多使用4个变量计数。之前已知的变量维数和数量的上限分别是14和15。

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The Weisfeiler-Leman dimension of planar graphs is at most 3

We prove that the Weisfeiler-Leman (WL) dimension of the class of all finite planar graphs is at most 3. In particular, every finite planar graph is definable in first-order logic with counting using at most 4 variables. The previously best known upper bounds for the dimension and number of variables were 14 and 15, respectively.

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2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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