Measurable chromatic and independence numbers for ergodic graphs and group actions

Measurable chromatic and independence numbers for ergodic graphs and group actions
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遍历图和群作用的可测量色数和独立数

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发表时间：
2013
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通讯作者：
A. Kechris
A. Kechris
中科院分区：
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作者：
Clinton T. Conley;A. Kechris

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本文研究了由下列条件生成的图的组合问题： 可数群在标准测度空间上的保测度作用特别是 我们研究色数和独立数，在测度论和Borel 上下文，并将这些参数的行为与作用基团的性质联系起来， 作为顺从性，Kazhdan的财产（T），和自由。我们还证明了Borel模拟的 有限组合学中关于群作用的经典布鲁克斯定理 形接头.
We study in this paper combinatorial problems concerning graphs generated by measure preserving actions of countable groups on standard measure spaces. In particular we study chromatic and independence numbers, in both the measure-theoretic and the Borel context, and relate the behavior of these parameters to properties of the acting group such as amenability, Kazhdan’s property (T), and freeness. We also prove a Borel analog of the classical Brooks’ Theorem in finite combinatorics for actions of groups with finitely many ends.