Results 1 to 10 of about 433,943 (319)
Cops and Robbers on 1-Planar Graphs [PDF]
International Symposium Graph Drawing and Network Visualization, 2023 Cops and Robbers is a well-studied pursuit-evasion game in which a set of cops seeks to catch a robber in a graph G, where cops and robber move along edges of G.
Stéphane Durocher +8 more
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Improvements on the density of maximal 1-planar graphs [PDF]
Journal of Graph Theory, 2015 A graph is 1‐planar if it can be drawn in the plane such that each edge is crossed at most once. A graph, together with a 1‐planar drawing is called 1‐plane.
János Barát, Gézá Tóth
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3D Visibility Representations of 1-planar Graphs [PDF]
International Symposium Graph Drawing and Network Visualization, 2017 We prove that every 1-planar graph G has a z-parallel visibility representation, i.e., a 3D visibility representation in which the vertices are isothetic disjoint rectangles parallel to the xy-plane, and the edges are unobstructed z-parallel visibilities
Patrizio Angelini +3 more
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Acyclic Chromatic Index of 1-Planar Graphs [PDF]
Mathematics, 2022 The acyclic chromatic index χa′(G) of a graph G is the smallest k for which G is a proper edge colorable using k colors. A 1-planar graph is a graph that can be drawn in plane such that every edge is crossed by at most one other edge.
Wanshun Yang +5 more
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The strong chromatic index of 1-planar graphs [PDF]
Discrete Mathematics & Theoretical Computer ScienceThe chromatic index $\chi'(G)$ of a graph $G$ is the smallest $k$ for which $G$ admits an edge $k$-coloring such that any two adjacent edges have distinct colors.
Yiqiao Wang +3 more
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On Drawings and Decompositions of 1-Planar Graphs [PDF]
The Electronic Journal of Combinatorics, 2013 A graph is called 1-planar if it can be drawn in the plane so that each of its edges is crossed by at most one other edge. We show that every 1-planar drawing of any 1-planar graph on $n$ vertices has at most $n-2$ crossings; moreover, this bound is ...
Július Czap, David E. Hudak
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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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Matchings in 1‐planar graphs with large minimum degree [PDF]
Journal of Graph Theory, 2021 In 1979, Nishizeki and Baybars showed that every planar graph with minimum degree 3 has a matching of size n3+c (where the constant c depends on the connectivity), and even better bounds hold for planar graphs with minimum degree 4 and 5.
Thérèse Biedl, John Wittnebel
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Joins of 1-planar graphs [PDF]
Acta Mathematica Sinica, English Series, 2014 A graph 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 1-planar graph joins. We prove that the join G + H is 1-planar if and only if the pair [G, H] is subgraph-majorized by one
J. Czap, Dávid Hudák, T. Madaras
semanticscholar +5 more sources
4-connected 1-planar chordal graphs are Hamiltonian-connected [PDF]
Journal of Graph TheoryTutte proved that 4‐connected planar graphs are Hamiltonian. It is unknown if there is an analogous result on 1‐planar graphs. In this paper, we characterize 4‐connected 1‐planar chordal graphs and show that all such graphs are Hamiltonian‐connected.
Licheng Zhang +3 more
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