Results 1 to 10 of about 30,007,210 (289)
Graph Planarity by Replacing Cliques with Paths †
Algorithms, 2020 This paper introduces and studies the following beyond-planarity problem, which we call h-Clique2Path Planarity. Let G be a simple topological graph whose vertices are partitioned into subsets of size at most h, each inducing a clique.
Alfredo Navarra +2 more
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Non-1-Planarity of Lexicographic Products of Graphs [PDF]
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
doaj +4 more sources
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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Packing Trees into 1-planar Graphs [PDF]
Journal of Graph Algorithms and Applications, 2021 We introduce and study the 1-planar packing problem: Given $k$ graphs with $n$ vertices $G_1, \dots, G_k$, find a 1-planar graph that contains the given graphs as edge-disjoint spanning subgraphs. We mainly focus on the case when each $G_i$ is a tree and
Felice De Luca +8 more
doaj +5 more sources
Parameterized Complexity of 1-Planarity [PDF]
Journal of Graph Algorithms and Applications, 2018 We consider the problem of drawing graphs with at most one crossing per edge. These drawings, and the graphs that can be drawn in this way, are called $1$-planar.
Michael Bannister +2 more
doaj +6 more sources
An annotated bibliography on 1-planarity [PDF]
Computer Science Review, 2017 The notion of 1-planarity is among the most natural and most studied generalizations of graph planarity. A graph is 1-planar if it has an embedding where each edge is crossed by at most another edge. The study of 1-planar graphs dates back to more than fifty years ago and, recently, it has driven increasing attention in the areas of graph theory, graph
Stephen Kobourov +2 more
exaly +5 more sources
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
doaj +3 more sources
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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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
openaire +3 more sources
Correction to: Outer 1-Planar Graphs [PDF]
Algorithmica, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Christopher Auer +6 more
openaire +1 more source