Results 41 to 50 of about 30,213,529 (145)
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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On (p, 1)-Total Labelling of Some 1-Planar Graphs
Discussiones Mathematicae Graph Theory, 2021 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, it is proved that the (p, 1)-total labelling number (p ≥ 2) of every 1-planar graph G is at most Δ(G) + 2p − 2 provided that Δ (G) ≥
Niu Bei, Zhang Xin
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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 Weak Flexibility in Planar Graphs [PDF]
, 2022 Recently, Dvořák, Norin, and Postle introduced flexibility as an extension of list coloring on graphs (J Graph Theory 92(3):191–206, 2019, https://doi.org/10.1002/jgt. 22447).
Murphy, Kyle +3 more
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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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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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Coloring count cones of planar graphs [PDF]
, 2022 For a plane near‐triangulation G with the outer face bounded by a cycle C, let nG⋆ denote the function that to each 4‐coloring ψ of C assigns the number of ways ψ extends to a 4‐coloring of G.
Lidicky, Bernard, Dvořák, Zdeněk
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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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Testing first-order properties for subclasses of sparse graphs [PDF]
, 2013 We present a linear-time algorithm for deciding first-order (FO) properties in classes of graphs with bounded expansion, a notion recently introduced by Nešetřil and Ossona de Mendez.
Thomas, Robin +2 more
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