Results 111 to 120 of about 30,213,529 (145)
On (p, 1)-total labelling of 1-planar graphs
Open Mathematics, 2011 Zhang Xin, Yu Yong, Liu Guizhen
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4-connected 1-planar chordal graphs are Hamiltonian-connected
Tutte proved that 4-connected planar graphs are Hamiltonian. It is unknown if there is an analogous result on 1-planar graphs. In this paper, we characterize 4-connected 1-planar chordal graphs, and show that all such graphs are Hamiltonian-connected.
Lv, Shengxiang +3 more
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Light edges in 1‐planar graphs
Journal of Graph Theory, 2022AbstractA 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 +2 more
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Algorithmica, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Christopher Auer +6 more
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Christopher Auer +6 more
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On the Pagenumber of 1-Planar Graphs
Chinese Annals of Mathematics, Series BzbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guan, Xiaxia, Yang, Weihua
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Remarks on the joins of 1-planar graphs
Applied Mathematics and Computation, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhangdong Ouyang, Jun Ge, Yichao Chen
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The Maximal 1-Planarity and Crossing Numbers of Graphs
Graphs and Combinatorics, 2021This 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 +2 more
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The Vertex Arboricity of 1-Planar Graphs
Graphs and CombinatoricszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dongdong Zhang +3 more
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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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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 MathematicsA 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 +2 more
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