Results 11 to 20 of about 20,236 (296)
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 [PDF]
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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Graph Planarity by Replacing Cliques with Paths [PDF]
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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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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Radial Level Planarity with Fixed Embedding [PDF]
Journal of Graph Algorithms and Applications, 2021 We study level planarity testing of graphs with a fixed combinatorial embedding for three different notions of combinatorial embeddings, namely the level embedding, the upward embedding and the planar embedding.
Guido Brückner, Ignaz Rutter
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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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Digital planarity—A review [PDF]
Discrete Applied Mathematics, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Valentin E. Brimkov +2 more
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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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