论无限正集的零因子图

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Soft Computing Pub Date : 2024-07-31 DOI:10.1007/s00500-024-09958-8

Radomír Halaš, Jozef Pócs

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引用次数: 0

摘要

众所周知，对于部分有序集，所谓的贝克猜想（即零因子图的有限簇数和色度数相等）是成立的 Halaš 和 Jukl (Discrete Math 309(13):4584-4589, 2009)。本文提出了这一事实的简单直接证明。此外，我们还研究了省略小群数有限性假设的情况。我们证明了猜想在一般情况下是不成立的，并提出了一系列反例。

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On zero-divisor graphs of infinite posets

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.

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来源期刊

Soft Computing 工程技术-计算机：跨学科应用

CiteScore

8.10

自引率

9.80%

发文量

927

审稿时长

7.3 months

期刊介绍： Soft Computing is dedicated to system solutions based on soft computing techniques. It provides rapid dissemination of important results in soft computing technologies, a fusion of research in evolutionary algorithms and genetic programming, neural science and neural net systems, fuzzy set theory and fuzzy systems, and chaos theory and chaotic systems. Soft Computing encourages the integration of soft computing techniques and tools into both everyday and advanced applications. By linking the ideas and techniques of soft computing with other disciplines, the journal serves as a unifying platform that fosters comparisons, extensions, and new applications. As a result, the journal is an international forum for all scientists and engineers engaged in research and development in this fast growing field.