Common graphs with arbitrary connectivity and chromatic number

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-09-01 DOI:10.1016/j.jctb.2023.06.001

Sejin Ko , Joonkyung Lee

引用次数: 6

Abstract

A graph H is common if the number of monochromatic copies of H in a 2-edge-colouring of the complete graph $K_{n}$ is asymptotically minimised by the random colouring. We prove that, given $k, r > 0$ , there exists a k-connected common graph with chromatic number at least r. The result is built upon the recent breakthrough of Kráľ, Volec, and Wei who obtained common graphs with arbitrarily large chromatic number and answers a question of theirs.

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具有任意连通性和色数的公共图

如果完整图Kn的2-色中H的单色副本的数量通过随机着色渐近最小化，则图H是常见的。我们证明，给定k，r>；0，存在一个色数至少为r的k-连通公共图。该结果建立在Kráľ、Volec和Wei最近的突破之上，他们获得了任意大色数的公共图，并回答了他们的一个问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.