色度编号不是赛事本地编号

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-10 DOI:10.1016/j.jctb.2024.04.005

António Girão , Kevin Hendrey , Freddie Illingworth , Florian Lehner , Lukas Michel , Michael Savery , Raphael Steiner

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引用次数: 0

摘要

斯科特（Scott）和西摩（Seymour）猜想存在这样一个函数 f:N→N：对于每个图 G 和同一顶点集上的锦标赛 T，χ(G)⩾f(k)意味着对于某个顶点 v，χ(G[NT+(v)])⩾k。在本注释中，我们推翻了这一猜想，即使 v 被大小为 O(log|V(G)|)的顶点集所替代。因此，我们否定地回答了 Harutyunyan、Le、Thomassé 和 Wu 提出的关于图 G 被另一个锦标赛取代时的相应问题，并推翻了 Nguyen、Scott 和 Seymour 提出的相关猜想。我们还证明，在色度数被退化性取代的情况下，会表现出截然不同的行为。

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Chromatic number is not tournament-local

Scott and Seymour conjectured the existence of a function $f : N \to N$ such that, for every graph G and tournament T on the same vertex set, $χ (G) ⩾ f (k)$ implies that $χ (G [N_{T}^{+} (v)]) ⩾ k$ for some vertex v. In this note we disprove this conjecture even if v is replaced by a vertex set of size $O (\log | V (G) |)$ . As a consequence, we answer in the negative a question of Harutyunyan, Le, Thomassé, and Wu concerning the corresponding statement where the graph G is replaced by another tournament, and disprove a related conjecture of Nguyen, Scott, and Seymour. We also show that the setting where chromatic number is replaced by degeneracy exhibits a quite different behaviour.

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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.