局部有限处处双端图的描述色数

IF 0.6 3区数学 Q3 MATHEMATICS

Groups Geometry and Dynamics Pub Date : 2020-04-05 DOI:10.4171/ggd/643

F. Weilacher

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引用次数: 3

摘要

我们构造了Borel图，它解决了描述图组合中的几个问题。这些问题包括“局部有限Borel图的Baire可测色数是否能超过通常的色数一个以上?”和“具有同构Cayley图的标记群的移位图是否具有相差一个以上的Borel色数?”对于连通分量都有两端的图，我们也给出了一个新的Borel色数界。

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Descriptive chromatic numbers of locally finite and everywhere two-ended graphs

We construct Borel graphs which settle several questions in descriptive graph combinatorics. These include "Can the Baire measurable chromatic number of a locally finite Borel graph exceed the usual chromatic number by more than one?" and "Can marked groups with isomorphic Cayley graphs have Borel chromatic numbers for their shift graphs which differ by more than one?" We also provide a new bound for Borel chromatic numbers of graphs whose connected components all have two ends.

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来源期刊

Groups Geometry and Dynamics 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Groups, Geometry, and Dynamics is devoted to publication of research articles that focus on groups or group actions as well as articles in other areas of mathematics in which groups or group actions are used as a main tool. The journal covers all topics of modern group theory with preference given to geometric, asymptotic and combinatorial group theory, dynamics of group actions, probabilistic and analytical methods, interaction with ergodic theory and operator algebras, and other related fields. Topics covered include: geometric group theory; asymptotic group theory; combinatorial group theory; probabilities on groups; computational aspects and complexity; harmonic and functional analysis on groups, free probability; ergodic theory of group actions; cohomology of groups and exotic cohomologies; groups and low-dimensional topology; group actions on trees, buildings, rooted trees.