Results 21 to 30 of about 107,869,965 (249)
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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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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Minimum Cycle Base of Graphs Identified by Two Planar Graphs [PDF]
, 2007 In this paper, we study the minimum cycle base of the planar graphs obtained from two 2-connected planar graphs by identifying an edge (or a cycle) of one graph with the corresponding edge (or cycle) of another, related with map geometries, i.e ...
Han, Ren, Dengju, Ma
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1-Visibility Representations of 1-Planar Graphs
Journal of Graph Algorithms and Applications, 2014 A 1-visibility representation of a graph displays each vertex as a horizontal vertex-segment, called a bar, and each edge as a vertical edge-segment between the segments of the vertices, such that each edge-segment crosses at most one vertex-segment and ...
Franz Brandenburg
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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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The complexity of two graph orientation problems [PDF]
, 2012 This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 ElsevierWe consider two orientation problems in a graph, namely the minimization of the sum of all the shortest path ...
Noble, SD +5 more
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1-Planarity of Graphs with a Rotation System
Journal of Graph Algorithms and Applications, 2015 A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once. 1-planarity is known NP-hard, even for graphs of bounded bandwidth, pathwidth, or treewidth, and for near-planar graphs in which an edge is added to a planar
Christopher Auer +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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Non-1-Planarity of Lexicographic Products of Graphs
Discussiones Mathematicae Graph Theory, 2021 In this paper, we show the non-1-planarity of the lexicographic product of a theta graph and K2. This result completes the proof of the conjecture that a graph G ◦ K2 is 1-planar if and only if G has no edge belonging to two cycles.
Matsumoto Naoki, Suzuki Yusuke
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Planar Graph Classifier - Class Information
, 2022 CSV files associating image files from the Planar Graph Classifier - Generated Graph Images (10.5281/zenodo.6510092) with planarity information.
Hummel, Matthias
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