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Mapping the structure-function landscape of semiconducting polymers.

Mater Horiz
Makki H, Burke C, Nielsen CB, Troisi A.
europepmc   +1 more source

An annotated bibliography on 1-planarity [PDF]

Computer Science Review, 2017
The notion of 1-planarity is among the most natural and most studied generalizations of graph planarity. A graph is 1-planar if it has an embedding where each edge is crossed by at most another edge. The study of 1-planar graphs dates back to more than fifty years ago and, recently, it has driven increasing attention in the areas of graph theory, graph
Stephen Kobourov, Fabrizio Montecchiani, Giuseppe Liotta   +2 more
exaly   +4 more sources

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Optimal 1-planar multigraphs

Discrete Mathematics, 2023
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Katsuya Sone, Yusuke Suzuki
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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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Majority choosability of 1-planar digraph

Czechoslovak Mathematical Journal, 2023
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Xia, Weihao, Wang, Jihui, Cai, Jiansheng
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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 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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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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