Results 131 to 140 of about 17,567 (164)

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 0002, Weifan Wang 0001   +2 more
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Outer 1-Planar Graphs

Algorithmica, 2015
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Christopher Auer, Christian Bachmaier, Franz J. Brandenburg, Andreas Gleißner, Kathrin Hanauer, Daniel Neuwirth, Josef Reislhuber   +6 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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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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The Vertex Arboricity of 1-Planar Graphs

Graphs and Combinatorics
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Dongdong Zhang, Juan Liu, Yongjie Li, Hehua Yang   +3 more
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Remarks on the joins of 1-planar graphs

Applied Mathematics and Computation, 2019
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Zhangdong Ouyang, Jun Ge, Yichao Chen
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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 0001, 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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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 0002, Jianfeng Wang 0002, Weifan Wang 0001   +2 more
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The Matching Extendability of Optimal 1-Planar Graphs

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