Local Coloring Problems on Smooth Graphs

无选择公理下的区分着色、正常着色与覆盖性质

Distinguishing colorings, proper colorings, and covering properties without the Axiom of Choice

本文在无选择公理的ZF集合论中证明若干关于无限局部有限连通图的色数、边色数、区分数与区分指数的命题等价于Kőnig引理，并给出与AC或Kőnig引理等价的覆盖与支配集存在性新条件。

分布式算法、Lovász局部引理与描述组合学

Distributed Algorithms, the Lovász Local Lemma, and Descriptive Combinatorics

该研究将有限组合学的分布式着色算法与对称Lovász局部引理拓展至Borel空间组合结构，得到良态着色的充分条件，为描述组合学与遍历理论提供新结论。

局部有限图着色参数的Brooks型定理与Konig引理

Brooks' type theorems for coloring parameters of locally finite graphs and Konig's Lemma

本文研究了无限局部有限连通图着色参数的Brooks型定理，证明其在ZF中不可证但可由Konig引理推导，并提出了与Konig引理等价的新着色参数存在条件，同时给出了ZFC下无限图列表可辨别色数的上界。

On Baire Measurable Colorings of Group Actions

The field of descriptive combinatorics investigates the question, to what extent can classical combinatorial results and techniques be made topologically or measure-theoretically well-behaved? This paper examines a class of coloring problems induced by actions of countable groups on Polish spaces, with the requirement that the desired coloring be Baire measurable. We show that the set of all such coloring problems that admit a Baire measurable solution for a particular free action $α$ is complete analytic (apart from the trivial situation when the orbit equivalence relation induced by $α$ is s…