The structure of k-planar graphs.Vida DujmovicPat MorinDavid R. Wood
If a graph G has a drawing in the plane in such a way that every two crossings are independent, then we call G a plane graph with independent crossings or IC-planar graph for short. In this paper, the structure of IC-planar graphs with minimum degree at least two or three is studied...
planar (ˈpleɪnə) adj 1.(Mathematics) of or relating to a plane 2.(Mathematics) lying in one plane; flat [C19: from Late Latinplānārison level ground, from Latinplānusflat] planarityn Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishe...
本期专栏为 “谱图理论” 系列的第26期,将介绍耶鲁大学教授、两届哥德尔奖得主 Daniel A. Spielman 所著图书 《Spectral and Algebraic Graph Theory》(电子版链接) 第二十六章 Ch 26: Planar Graphs 2, the Co…
摘要: Dirac (1962) showed that the planar graphs with no prism minor are the graphs obtainable by 2-sums from bonds, cycles, wheels and K 5\ e 's. We give a new characterization of these graphs in terms of an optimization problem defined on the cycle bases of a graph....
In particular, a 1-planar graph is IC-planar if it admits a 1-planar drawing such that no two crossed edges share an end-vertex. A 1-planar graph is NIC-planar if it admits a 1-planar drawing such that any two distinct pairs of crossing edges have at most one end-vertex in common...
Spielman 所著图书 《Spectral and Algebraic Graph Theory》(电子版链接) 第二十五章 Ch 25: The Second Eigenvalue of Planar Graphs 中的内容。 本期作者 | 陈靖宇,中国人民大学高瓴人工智能学院 25.1 本节概述 谱图理论首先引起研究人员的广泛关注的原因之一是其成功地使用第二个拉普拉斯特征向量来划分平面图...
The node cost measure for embedding graphs on the planar grid (Extended Abstract) The two major cost measures used in the past for grid embeddings are area (or the area of the smallest square or rectangle that contains the embedding) and......
Structure of urban movements: polycentric activity and entangled hierarchical flows. PLoS ONE 6, e15923 (2011). Article Google Scholar SteadieSeifi, M., Dellaert, N. P., Nuijten, W., Van Woensel, T. & Raoufi, R. Multimodal freight transportation planning: a literature review. Eur. J. ...
State-of-the-art tensor-based approaches29 have been used to simulate larger circuits but are ineffective in the case of nonplanar graphs. Another very important tensor-based method is the Matrix Product State (MPS) variational representation of the many-qubit state. This is is a low-...