Results 11 to 20 of about 13,317 (263)
Heuristics for Exact 1-Planarity Testing
Journal of Graph Algorithms and ApplicationsSince many real-world graphs are nonplanar, the study of graphs that allow few crossings per edge has been an active subfield of graph theory in recent years.
Miriam Münch +3 more
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On Morphing 1-Planar Drawings [PDF]
, 2021 Computing a morph between two drawings of a graph is a classical problem in computational geometry and graph drawing. While this problem has been widely studied in the context of planar graphs, very little is known about the existence of topology-preserving morphs for pairs of non-planar graph drawings.
Patrizio Angelini +3 more
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Correction to: Outer 1-Planar Graphs [PDF]
Algorithmica, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Christopher Auer +6 more
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On the Sizes of Bipartite 1-Planar Graphs [PDF]
The Electronic Journal of Combinatorics, 2021 A graph is called $1$-planar if it admits a drawing in the plane such that each edge is crossed at most once. Let $G$ be a bipartite $1$-planar graph with $n$ ($n\ge 4$) vertices and $m$ edges. Karpov showed that $m\le 3n-8$ holds for even $n\ge 8$ and $m\le 3n-9$ holds for odd $n\ge 7$.
Yuanqiu Huang +2 more
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Counting cliques in 1-planar graphs
European Journal of Combinatorics, 2023 The problem of maximising the number of cliques among n-vertex graphs from various graph classes has received considerable attention. We investigate this problem for the class of 1-planar graphs where we determine precisely the maximum total number of cliques as well as the maximum number of cliques of any fixed size. We also precisely characterise the
Jochen Pascal Gollin +4 more
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The Stub Resolution of 1-Planar Graphs
Journal of Graph Algorithms and Applications, 2020 The resolution of a drawing plays a crucial role when defining criteria for its quality. In the past, grid resolution, edge-length resolution, angular resolution and crossing resolution have been investigated. In this paper, we investigate the stub resolution, a recently introduced criterion for nonplanar drawings. Intersection points divide edges into
Michael Kaufmann 0001 +5 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 tight.
Július Czap, Dávid Hudák
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The structure of 1-planar graphs
Discrete Mathematics, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Igor Fabrici, Tomás Madaras
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On edge colorings of 1-planar graphs [PDF]
Information Processing Letters, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xin Zhang 0017, Jianliang Wu 0001
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Cops and Robbers on 1-Planar Graphs
, 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. The cop number of G is the minimum number of cops that is sufficient to catch the robber. Every planar graph has cop number at most three, and there are planar graphs for which three cops are ...
Stephane Durocher +8 more
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