Results 241 to 250 of about 28,550 (268)
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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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Fáry’s Theorem for 1-Planar Graphs
2012A 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 +3 more
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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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The Matching Extendability of Optimal 1-Planar Graphs
Graphs and Combinatorics, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jun Fujisawa +2 more
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The 6-degeneracy of 1-planar graphs
Discrete Applied MathematicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Qingqin Wu +2 more
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On the Equitable Edge-Coloring of 1-Planar Graphs and Planar Graphs
Graphs and Combinatorics, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Daiqiang Hu +3 more
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Algorithms for 1-Planar Graphs
2020A 1-planar graph is a graph that can be embedded in the plane with at most one crossing per edge. It is known that testing 1-planarity of a graph is NP-complete. This chapter reviews the algorithmic results on 1-planar graphs. We first review a linear time algorithm for testing maximal 1-planarity of a graph if a rotation system (i.e., the circular ...
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Interval valued m-polar fuzzy planar graph and its application
Artificial Intelligence Review, 2020Tanmoy Mahapatra +2 more
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The maximum number of paths of length four in a planar graph
Discrete Mathematics, 2021Debarun Ghosh +2 more
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The Alon-Tarsi number of a planar graph minus a matching
Journal of Combinatorial Theory Series B, 2020Jarosław Grytczuk, Xuding Zhu
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