在几条线和几面上绘制图形的复杂性

Q3 Mathematics

Journal of Graph Algorithms and Applications Pub Date : 2023-01-01 DOI:10.7155/jgaa.00630

Steven Chaplick, Krzysztof Fleszar, Fabian Lipp, Alexander Ravsky, Oleg Verbitsky, Alexander Wolff

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引用次数: 0

摘要

众所周知，在$\mathbb{R}^3$中，任何图都可以画出无交叉的直线;在$\mathbb{R}^2$中，任何平面图都可以画出无交叉的直线。对于图$G$和$d $在\{2,3\}$中，设$\rho^1_d(G)$表示$\mathbb{R}^d$中能够覆盖$G$的所有边的最小行数。对于$d=2$， $G$必须是平面的。我们研究了计算这些参数的复杂性，并得到了以下硬度和算法结果。

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The Complexity of Drawing Graphs on Few Lines and Few Planes

It is well known that any graph admits a crossing-free straight-line drawing in $\mathbb{R}^3$ and that any planar graph admits the same even in $\mathbb{R}^2$. For a graph $G$ and $d \in \{2,3\}$, let $\rho^1_d(G)$ denote the minimum number of lines in $\mathbb{R}^d$ that together can cover all edges of a drawing of $G$. For $d=2$, $G$ must be planar. We investigate the complexity of computing these parameters and obtain the following hardness and algorithmic results.

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来源期刊

Journal of Graph Algorithms and Applications Mathematics-Geometry and Topology

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

50 weeks

期刊介绍： The Journal of Graph Algorithms and Applications (JGAA) is a peer-reviewed scientific journal devoted to the publication of high-quality research papers on the analysis, design, implementation, and applications of graph algorithms. JGAA is supported by distinguished advisory and editorial boards, has high scientific standards and is distributed in electronic form. JGAA is a gold open access journal that charges no author fees. Topics of interest for JGAA include but are not limited to: Design and analysis of graph algorithms: exact and approximation graph algorithms; centralized and distributed graph algorithms; static and dynamic graph algorithms; internal- and external-memory graph algorithms; sequential and parallel graph algorithms; deterministic and randomized graph algorithms. Experiences with graph and network algorithms: animations; experimentations; implementations. Applications of graph and network algorithms: biomedical informatics; computational biology; computational geometry; computer graphics; computer-aided design; computer and interconnection networks; constraint systems; databases; economic networks; graph drawing; graph embedding and layout; knowledge representation; multimedia; social networks; software engineering; telecommunication networks; user interfaces and visualization; VLSI circuits.