Results 21 to 30 of about 28,812 (264)
Bar 1-Visibility Graphs and their relation to other Nearly Planar Graphs
Journal of Graph Algorithms and Applications, 2014 A graph is called a strong (resp. weak) bar 1-visibility graph if its vertices can be represented as horizontal segments (bars) in the plane so that its edges are all (resp.
William Evans +4 more
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The structure of 1-planar graphs
Discrete Mathematics, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Igor Fabrici, Tomás Madaras
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On edge colorings of 1-planar graphs [PDF]
Information Processing Letters, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xin Zhang 0017, Jianliang Wu 0001
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On Aligned Bar 1-Visibility Graphs
Journal of Graph Algorithms and Applications, 2017 A graph is called a bar 1-visibility graph if its vertices can be represented as horizontal segments, called bars, and each edge corresponds to a vertical line of sight which can traverse another bar.
Franz Brandenburg +2 more
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Acyclic colouring of 1-planar graphs
Discrete Applied Mathematics, 2001 A graph is said to be 1-planar if it can be embedded into the plane so that each of its edges is crossed by at most one other edge. A coloring of the vertices of a graph is said to be acyclic if every cycle contains at least three colors. The acyclic chromatic number \(a(G)\) of a graph \(G\) is the minimal \(k\) such that \(G\) admits an acyclic \(k\)-
Oleg V. Borodin +3 more
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Drawing outer-1-planar graphs revisited
Journal of Graph Algorithms and Applications, 2022 In a recent article (Auer et al., Algorithmica 2016) it was claimed that every outer-1-planar graph has a planar visibility representation of area $O(n\log n)$.
Therese Biedl
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On total colorings of 1-planar graphs [PDF]
Journal of Combinatorial Optimization, 2013 A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, we confirm the total-coloring conjecture for 1-planar graphs with maximum degree at least 13.
Xin Zhang 0017 +2 more
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Drawing Outer 1-planar Graphs with Few Slopes
Journal of Graph Algorithms and Applications, 2015 A graph is outer 1-planar if it admits a drawing where each vertex is on the outer face and each edge is crossed by at most another edge. Outer 1-planar graphs are a superclass of the outerplanar graphs and a subclass of the planar partial 3-trees.
Emilio Di Giacomo +2 more
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On the Density of Maximal 1-Planar Graphs [PDF]
, 2013 A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once. It is maximal 1-planar if the addition of any edge violates 1-planarity. Maximal 1-planar graphs have at most 4n−8 edges. We show that there are sparse maximal 1-planar graphs with only $\frac{45}{17} n + \mathcal{O}(1)$ edges.
Franz-Josef Brandenburg +5 more
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Unique Triangulated 1-Planar Graphs
CoRR, 2023 It is well-known that every 3-connected planar graph has a unique planar embedding on the sphere. We study the extension to triangulated 1-planar graphs, T1P graphs for short, which admit an embedding in which each edge is crossed at most once and each face is a triangle, and obtain an algorithmic solution by a cubic time recognition algorithm that ...
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