Some new results on bar visibility of digraphs

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-10-01 DOI:10.1016/j.dam.2024.09.024

Yuanrui Feng , Jun Ge , Douglas B. West , Yan Yang

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引用次数: 0

Abstract

Visibility representation of digraphs was introduced by Axenovich et al. (2013) as a natural generalization of

t

-bar visibility representation of undirected graphs. A

t

-bar visibility representation of a digraph

G

assigns each vertex at most

t

horizontal bars in the plane so that there is an arc

x y

in the digraph if and only if some bar for

x

“sees” some bar for

y

above it along an unblocked vertical strip with positive width. The visibility number

b (G)

is the least

t

such that

G

has a

t

-bar visibility representation. In this paper, we solve several problems about

b (G)

posed by Axenovich et al. and prove that determining whether the bar visibility number of a digraph is 2 is NP-complete.

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关于条形图可见性的一些新结果

数图的可见性表示是由 Axenovich 等人（2013 年）提出的，是对无向图的 t 条可见性表示的自然概括。数图 G 的 t 条可见度表示法为每个顶点在平面上分配了最多 t 条水平条，因此当且仅当 x 的某个条沿着宽度为正的无阻挡垂直条 "看到 "其上方 y 的某个条时，数图中才有弧 xy。可见度数 b(G) 是 G 具有 t 条可见度表示的最小 t。在本文中，我们解决了阿克森诺维奇等人提出的几个关于 b(G) 的问题，并证明确定一个数图的条形可见度数是否为 2 是 NP-完全的。

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.