Results 1 to 10 of about 13,317 (263)
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
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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
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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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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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A GRAPH ASSOCIATED TO FILTERS OF A LATTICE [PDF]
Journal of Algebraic Systems, 2023 Let $L$ be a lattice with the least element $0$ and the greatest element $1$. In this paper, we associate a graph to filters of $L$, in which the vertex set is being the set of all non-trivial filters of $L$, and two distinct vertices $F$ and $E$ are ...
Sh. Ebrahimi Atani +3 more
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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.
Patrizio Angelini +7 more
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N-(4-Hydroxy-2-nitrophenyl)acetamide
IUCrData, 2022 The title compound, C8H8N2O4, differs in its degree of planarity from the 3-nitro isomer and also in its hydrogen-bonding pattern. Its NH group forms an intramolecular hydrogen bond to a nitro oxygen atom, and its OH group forms an intermolecular ...
James E. Hines III +3 more
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Journal of Biological Engineering, 2020 Background In current cancer spheroid culturing methods, the transfer and histological processing of specimens grown in 96-well plates is a time consuming process.
Warren Weisler +4 more
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Discrete Mathematics & Theoretical Computer ScienceNot every directed acyclic graph (DAG) whose underlying undirected graph is planar admits an upward planar drawing. We are interested in pushing the notion of upward drawings beyond planarity by considering upward $k$-planar drawings of DAGs in which the
Patrizio Angelini +10 more
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Acta Crystallographica Section E: Crystallographic Communications, 2022 In the molecule of the title compound, C9H11N5O2, the oxime and hydrazide groups are situated in a cis-position in relation to the C—C bond linking the two functional groups.
Maksym O. Plutenko +4 more
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