Minimal definable graphs of definable chromatic number at least three

被引：4

作者：

Carroy, Raphael ^{[1
]}

Miller, Benjamin D. ^{[2
]}

Schrittesser, David ^{[2
]}

Vidnyanszky, Zoltan ^{[2
,3
]}

机构：

[1] Univ Torino Palazzo Campana, Dipartimento Matemat Giuseppe Peano, Via Carlo Alberto 10, I-10123 Turin, Italy

[2] Univ Vienna, Dept Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

[3] CALTECH, Dept Math, Pasadena, CA 91125 USA

来源：

FORUM OF MATHEMATICS SIGMA | 2021年 / 9卷

基金：

奥地利科学基金会;

关键词：

Borel bipartite; Borel coloring; INFINITE;

D O I：

10.1017/fms.2020.58

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that there is a Borel graph on a standard Borel space of Borel chromatic number three that admits a Borel homomorphism to every analytic graph on a standard Borel space of Borel chromatic number at least three. Moreover, we characterize the Borel graphs on standard Borel spaces of vertex-degree at most two with this property and show that the analogous result for digraphs fails.

引用

页数：16

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