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Synchronized Planarity with Applications to Constrained Planarity Problems [PDF]

ACM Transactions on Algorithms, 2023
We introduce the problem Synchronized Planarity. Roughly speaking, its input is a loop-free multi-graph together with synchronization constraints that, e.g., match pairs of vertices of equal degree by providing a bijection between their edges ...
Simon D Fink, Ignaz Rutter, Thomas Bläsius   +2 more
exaly   +2 more sources

Beyond level planarity: Cyclic, torus, and simultaneous level planarity

Theoretical Computer Science, 2020
In this paper we settle the computational complexity of two open problems related to the extension of the notion of level planarity to surfaces different from the plane. Namely, we show that the problems of testing the existence of a level embedding of a
Fabrizio Frati, Maurizio Patrignani, Ignaz Rutter   +2 more
exaly   +2 more sources

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Optimal 1-planar multigraphs

Discrete Mathematics, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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
openaire   +1 more source

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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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 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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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
openaire   +3 more sources