Results 271 to 280 of about 27,017 (285)

Light edges in 1‐planar graphs

Journal of Graph Theory, 2022
AbstractA graph is 1‐planar if it can be drawn in the plane so that each edge is crossed by at most one other edge. In this paper, we prove that every 1‐planar graph with minimum degree at least 3 contains an edge with such that one of the following holds: (1) and ; (2) and ; (3) and ; (4) and ; (5) .
Juan Liu, Yiqiao Wang, Weifan Wang
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Outer 1-Planar Graphs

Algorithmica, 2015
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Auer, Christopher, Bachmaier, Christian, Brandenburg, Franz J., Gleißner, Andreas, Hanauer, Kathrin, Neuwirth, Daniel, Reislhuber, Josef   +6 more
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The Maximal 1-Planarity and Crossing Numbers of Graphs

Graphs and Combinatorics, 2021
This paper deals with 1-planar graphs and their crossing number. A 1-planar graph is a graph that has a drawing on the plane where each edge has at most one crossing. Hence, a 1-planar graph is a superfamily of planar graphs. It is known, due to a result by \textit{J. Czap} and \textit{D. Hudák} [Electron. J. Comb. 20, No.
Zhangdong Ouyang, Yuanqiu Huang, Fengming Dong   +2 more
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On the Pagenumber of 1-Planar Graphs

Chinese Annals of Mathematics, Series B
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Guan, Xiaxia, Yang, Weihua
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Fáry’s Theorem for 1-Planar Graphs

2012
A plane graph is a graph embedded in a plane without edge crossings. Fary’s theorem states that every plane graph can be drawn as a straight-line drawing, preserving the embedding of the plane graph. In this paper, we extend Fary’s theorem to a class of non-planar graphs.
Seok-Hee Hong, Peter Eades, Giuseppe Liotta, Sheung-Hung Poon   +3 more
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1-Planar Graphs

2020
Topological graph theory discusses, in most cases, graphs embedded in the plane (or other surfaces). For example, such plane graphs are sometimes regarded as the simplest town maps. Now, we consider a town having some pedestrian bridges, which cannot be realized by a plane graph. Its underlying graph can actually be regarded as a 1-plane graph.
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On the Equitable Edge-Coloring of 1-Planar Graphs and Planar Graphs

Graphs and Combinatorics, 2017
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Hu, Dai-Qiang, Wu, Jian-Liang, Yang, Donglei, Zhang, Xin   +3 more
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The Vertex Arboricity of 1-Planar Graphs

Graphs and Combinatorics
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Zhang, Dongdong, Liu, Juan, Li, Yongjie, Yang, Hehua   +3 more
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Linear Arboricity of Outer-1-Planar Graphs

Journal of the Operations Research Society of China, 2019
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Xin Zhang, Bi Li
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The Matching Extendability of Optimal 1-Planar Graphs

Graphs and Combinatorics, 2018
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Fujisawa, Jun, Segawa, Keita, Suzuki, Yusuke   +2 more
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