Results 11 to 20 of about 433,943 (319)
Bar 1-Visibility Drawings of 1-Planar Graphs
International Conference on Applied Algorithms, 2013 A bar 1-visibility drawing of a graph G is a drawing of G where each vertex is drawn as a horizontal line segment called a bar, each edge is drawn as a vertical line segment between its incident vertices such that each edge crosses at most one bar.
Shaheena Sultana +3 more
semanticscholar +5 more sources
Right Angle Crossing Graphs and 1-Planarity [PDF]
Discrete Applied Mathematics, 2011 A Right Angle Crossing Graph (also called RAC graph for short) is a graph that has a straight-line drawing where any two crossing edges are orthogonal to each other. A 1-planar graph is a graph that has a drawing where every edge is crossed at most once.
Peter Eades, Giuseppe Liotta
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On 1-Planar Graphs with Bounded Cop-Number [PDF]
Theoretical Computer ScienceCops and Robbers is a type of pursuit-evasion game played on a graph where a set of cops try to capture a single robber. The cops first choose their initial vertex positions, and later the robber chooses a vertex. The cops and robbers make their moves in alternate turns: in the cops' turn, every cop can either choose to move to an adjacent vertex or ...
Prosenjit Bose +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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Equitable Coloring in 1-Planar Graphs
Discrete Mathematics, 2023 9 ...
Daniel W. Cranston, Reem Mahmoud
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Unique Triangulated 1-Planar Graphs
arXiv.org, 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 ...
F. Brandenburg
semanticscholar +3 more sources
Discrete Mathematics, 2007 AbstractA graph is 1-planar if it can be drawn on the plane so that each edge is crossed by no more than one other edge. A non-1-planar graph G is minimal if the graph G-e is 1-planar for every edge e of G. We prove that there are infinitely many minimal non-1-planar graphs (MN-graphs). It is known that every 6-vertex graph is 1-planar.
Vladimir P. Korzhik
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Bondage Number of 1-Planar Graph
Applied Mathematics, 2010 The bondage number of a nonempty graph G is the cardinality of a smallest set of edges whose removal from G results in a graph a domination number greater than the domination number of G. In this paper, we prove that for a 1-planar graph G.
Qiaoling Ma, Sumei Zhang, Jihui Wang
semanticscholar +4 more sources
Discrete Applied Mathematics, 2014 A graph is 1-planar if it can be drawn in the plane such that each of its edges is crossed at most once. We prove a conjecture of Czap and Hudak (2013) stating that the edge set of every 1-planar graph can be decomposed into a planar graph and a forest.
Eyal Ackerman
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Orthogonal and Smooth Orthogonal Layouts of 1-Planar Graphs with Low Edge Complexity
International Symposium Graph Drawing and Network Visualization, 2018 While orthogonal drawings have a long history, smooth orthogonal drawings have been introduced only recently. So far, only planar drawings or drawings with an arbitrary number of crossings per edge have been studied. Recently, a lot of research effort in
Evmorfia N. Argyriou +7 more
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