Results 251 to 260 of about 200,785 (277)

Algorithms for 1-Planar Graphs

2020
A 1-planar graph is a graph that can be embedded in the plane with at most one crossing per edge. It is known that testing 1-planarity of a graph is NP-complete. This chapter reviews the algorithmic results on 1-planar graphs. We first review a linear time algorithm for testing maximal 1-planarity of a graph if a rotation system (i.e., the circular ...
openaire   +1 more source

Incidence Coloring of Outer-1-planar Graphs

Acta Mathematicae Applicatae Sinica, English Series
A proper incidence $k$-coloring of a graph $G$ is a coloring of the incidences using $k$ colors in such a way that every two adjacent incidences have distinct colors. The minimum integer $k$ such that $G$ has a proper incidence $k$-coloring is the incidence chromatic number of $G$, denoted by $\chi_{i}(G)$.
Qi, Mengke, Zhang, Xin
openaire   +1 more source

On the Pagenumber of 1-Planar Graphs

Chinese Annals of Mathematics, Series B
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guan, Xiaxia, Yang, Weihua
openaire   +1 more source

The Vertex Arboricity of 1-Planar Graphs

Graphs and Combinatorics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Dongdong, Liu, Juan, Li, Yongjie, Yang, Hehua   +3 more
openaire   +2 more sources

Spectral extrema of 1-planar graphs

Discrete Mathematics
A graph is \(1\)-planar if it can be drawn in the plane such that each of its edges is crossed at most once. The authors study the spectral radius (i.e., largest eigenvalue of the adjacency matrix) of \(1\)-planar graphs. Firstly, an upper bound \(5+\sqrt{2n+5}\) is given for the spectral radius of an \(n\)-vertex \(1\)-planar graph with \(n\ge 7 ...
Wenqian Zhang, Jianfeng Wang, Weifan Wang   +2 more
openaire   +2 more sources

The Matching Extendability of Optimal 1-Planar Graphs

Graphs and Combinatorics, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fujisawa, Jun, Segawa, Keita, Suzuki, Yusuke   +2 more
openaire   +1 more source

Note on improper coloring of $1$-planar graphs

Czechoslovak Mathematical Journal, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chu, Yanan, Sun, Lei, Yue, Jun
openaire   +2 more sources

The critical role of composition-dependent intragrain planar defects in the performance of MA1–xFAxPbI3 perovskite solar cells

Nature Energy, 2021
Wei Li, Mathias Uller Rothmann, Ye Zhu
exaly  

A quick guide to (transmembrane) planar cell polarity mouse strains

Nature Reviews Molecular Cell Biology, 2023
Sarah V Paramore
exaly  

Planar gradient metamaterials

Nature Reviews Materials, 2016
Yadong Xu, Yangyang Fu, Huanyang Chen
exaly