Graphs with Geometric Representations

具有几何表示的图形

• 批准号: 299431151
• 负责人: Professor Dr. Stefan Felsner
• 金额: --
• 依托单位: Fachgebiet Diskrete Mathematik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2018-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/299431151?language=en
• 关键词: Graphs; Geometric; Representations

The interplay of graphs and geometric representations has two aspects that lead to different types of problem. Type 1, is to start withsome graph and ask whether he admits a representation in a prescribed model of geometric realization. Type 2, is to start with a geometric configuration and ask about properties of some graphs induced by the configuration. In the proposed project we are interested in problems of both types. To group them we establish two research areas I. Geometric representations of planar graphs. II. Intersection representations and order. Each areas has three subareas. We have grouped problems from each of the subareas that are to be addressed within the project. Some of the problems are well known and assumed to be hard. Their solution will have impact for other fields.

图形和几何表示的相互作用有两个方面，导致不同类型的问题。类型1，是从某个图开始，并询问他是否承认几何实现的规定模型中的表示。类型2，是从一个几何构型开始，并询问由该构型诱导的一些图的性质。在拟议的项目中，我们对这两种类型的问题都感兴趣。为了将它们分类，我们建立了两个研究领域。平面图的几何表示。二.交叉表示和顺序。每个区域有三个子区域。我们将项目中要解决的每个子领域的问题进行了分组。其中一些问题是众所周知的，并被认为是困难的。他们的解决方案将对其他领域产生影响。

项目成果

Boolean Dimension and Tree-Width

布尔维度和树宽度

• DOI: 10.1007/s00493-020-4000-9
• 发表时间: 2020
• 期刊: Combinatorica
• 影响因子: 1.1
• 作者: S. Felsner;T. Mészáros;P. Micek
• 通讯作者: P. Micek

4-Connected Triangulations on Few Lines

几条线上的 4 连通三角剖分

• DOI: 10.1007/978-3-030-35802-0_30
• 发表时间: 2019
• 作者: S. Felsner

Separating tree-chromatic number from path-chromatic number

将树色数与路径色数分开

• DOI: 10.1016/j.jctb.2019.02.003
• 发表时间: 2019
• 期刊: J. Comb. Theory, Ser. B
• 作者: F. Barrera-Cruz;S. Felsner;T. Mészáros;P. Micek;H. Smith;L. Taylor;W. T. Trotter
• 通讯作者: W. T. Trotter