On zero-divisor graphs of infinite posets

被引：0
|
作者：
Halaš, Radomír [1 ]
Pócs, Jozef [1 ,2 ]
机构：
[1] Department of Algebra and Geometry, Faculty of Science Palacký University Olomouc, 17. listopadu 12, Olomouc,771 46, Czech Republic
[2] Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, Košice,040 01, Slovakia
来源：
Soft Computing | 2024年 / 28卷 / 20期
关键词：
Set theory;
D O I：
10.1007/s00500-024-09958-8
中图分类号：
学科分类号：
摘要：
It is known that the so-called Beck’s conjecture, i.e. the equality of the finite clique and chromatic numbers of a zero-divisor graph, holds for partially ordered sets Halaš and Jukl (Discrete Math 309(13):4584–4589, 2009). In this paper we present a simple direct proof of this fact. Also, the case when the finiteness assumption of the clique number is omitted is investigated. We have shown that the conjecture fails in general and a bunch of counterexamples is presented. © The Author(s) 2024.
引用
收藏
页码：12113 / 12118
页数：5
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