Results 11 to 20 of about 22,383 (289)
Journal of Graph Algorithms and Applications, 2021 In this paper, we introduce and study multilevel planarity, a generalization of upward planarity and level planarity. Let $G = (V, E)$ be a directed graph and let $\ell: V \to \mathcal P(\mathbb Z)$ be a function that assigns a finite set of integers ...
Lukas Barth +3 more
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Toward a Theory of Planarity: Hanani-Tutte and Planarity Variants
Journal of Graph Algorithms and Applications, 2013 We study Hanani-Tutte style theorems for various notions of planarity, including partially embedded planarity and simultaneous planarity. This approach brings together the combinatorial, computational and algebraic aspects of planarity notions and may ...
Marcus Schaefer
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On the Planarity of Graphs Associated with Symmetric and Pseudo Symmetric Numerical Semigroups
Mathematics, 2023 Let S(m,e) be a class of numerical semigroups with multiplicity m and embedding dimension e. We call a graph GS an S(m,e)-graph if there exists a numerical semigroup S∈S(m,e) with V(GS)={x:x∈g(S)} and E(GS)={xy⇔x+y∈S}, where g(S) denotes the gap set of S.
Yongsheng Rao +2 more
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Constrained Planarity in Practice -- Engineering the Synchronized Planarity Algorithm [PDF]
Journal of Graph Algorithms and ApplicationsIn the constrained planarity setting, we ask whether a graph admits a planar drawing that additionally satisfies a given set of constraints. These constraints are often derived from very natural problems; prominent examples are Level Planarity, where ...
Simon Dominik Fink, Ignaz Rutter
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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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Near-planar light outcoupling structures with finite lateral dimensions for ultra-efficient and optical crosstalk-free OLED displays [PDF]
Nature CommunicationsThe stratified structure of organic light-emitting diodes (OLEDs) confines much of the generated light within substrates or organic layers, limiting outcoupling to air.
MinJae Kim, Junho Kim, Seunghyup Yoo
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2-PROPIONYLTHIOPHENE: PLANAR, OR NOT PLANAR, THAT IS THE QUESTION [PDF]
Proceedings of the 2021 International Symposium on Molecular Spectroscopy, 2020 Non-planarity of 2-propionylthiophene proven by the microwave spectroscopy – quantum chemistry duet.
Dindic, Christina +2 more
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2,3-Dihydro-1H-cyclopenta[b]naphthalene-4,9-dione
IUCrData, 2021 The title compound, C13H10O2, crystallizes with two almost planar molecules in the asymmetric unit. In the crystal, slipped π–π stacking interactions help to establish the packing with the shortest centroid–centroid separation being 3.8195 (18) Å.
Sambasivarao Kotha +2 more
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Two Simple and Reliable Metrics of Molecular Planarity: Molecular Planarity Parameter (MPP) and Span of Deviation from Plane (SDP) [PDF]
, 2021 Planarity is a very important structural character of molecules, which is closely related to many molecular properties. However, there is currently no simple, universal, and robust way to measure molecular planarity. In order to fill this evident gap, we
Tian, Lu
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Planarity of Inclusion Graph of Cyclic Subgroups of Finite Group [PDF]
Mathematics Interdisciplinary Research, 2020 Let G be a finite group. The inclusion graph of cyclic subgroups of G, Ic(G), is the (undirected) graph with vertices of all cyclic subgroups of G, and two distinct cyclic subgroups ⟨a⟩ and ⟨b⟩, are adjacent if and only if ⟨a⟩ ⊂ ⟨b⟩ or ⟨b⟩ ⊂ ⟨a⟩. In this
Zahra Garibbolooki, Sayyed Heidar Jafari
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