Results 31 to 40 of about 17,567 (164)
Recognizing IC-Planar and NIC-Planar Graphs
Journal of Graph Algorithms and Applications, 2018 We prove that triangulated IC-planar graphs and triangulated $K_5$-free or $X4W$-free NIC-planar graphs can be recognized in cubic time. A graph is 1-planar if it can be drawn in the plane with at most one crossing per edge.
Franz Brandenburg
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Drawing Subcubic 1-Planar Graphs with Few Bends, Few Slopes, and Large Angles
Journal of Graph Algorithms and Applications, 2021 We show that the $1$-planar slope number of $3$-connected cubic $1$-planar graphs is at most four when edges are drawn as polygonal curves with at most one bend each, that is, any such graph admits a drawing with at most one bend per edge and such that ...
Philipp Kindermann +3 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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Non 1-planarity of lexicographic products of graphs
Discussiones Mathematicae Graph Theory, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Matsumoto Naoki, Suzuki Yusuke
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On An Extremal Problem In The Class Of Bipartite 1-Planar Graphs
Discussiones Mathematicae Graph Theory, 2016 A graph G = (V, E) is called 1-planar if it admits a drawing in the plane such that each edge is crossed at most once. In this paper, we study bipartite 1-planar graphs with prescribed numbers of vertices in partite sets.
Czap Július +2 more
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Discrete Applied Mathematics, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Right Angle Crossing Graphs and 1-Planarity [PDF]
Discrete Applied Mathematics, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Eades Peter, LIOTTA, Giuseppe
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A note on odd colorings of 1-planar graphs
Discrete Applied Mathematics, 2023 A proper coloring of a graph is odd if every non-isolated vertex has some color that appears an odd number of times on its neighborhood. This notion was recently introduced by Petruševski and Škrekovski, who proved that every planar graph admits an odd $9$-coloring; they also conjectured that every planar graph admits an odd $5$-coloring. Shortly after,
Daniel W. Cranston +2 more
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On the Maximum Independent Set Problem in Subclasses of Planar Graphs
Journal of Graph Algorithms and Applications, 2010 The maximum independent set problem is known to be NP-hard in the class of planar graphs. In the present paper, we study its complexity in hereditary subclasses of planar graphs.
Vadim Lozin, Martin Milanič
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