Results 31 to 40 of about 30,007,210 (289)
Acyclic colouring of 1-planar graphs
Discrete Applied Mathematics, 2001 A graph is said to be 1-planar if it can be embedded into the plane so that each of its edges is crossed by at most one other edge. A coloring of the vertices of a graph is said to be acyclic if every cycle contains at least three colors. The acyclic chromatic number \(a(G)\) of a graph \(G\) is the minimal \(k\) such that \(G\) admits an acyclic \(k\)-
Oleg V. Borodin +3 more
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Toward a Theory of Planarity: Hanani-Tutte and Planarity Variants
, 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 ...
Schaefer, Marcus, Marcus Schaefer
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, 2016 In this paper we settle the computational complexity of two open problems related to the extension of the notion of level planarity to surfaces different from the plane. Namely, we show that the problems of testing the existence of a level embedding of a
Nöllenburg, M. +7 more
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Constrained Planarity in Practice -- Engineering the Synchronized Planarity Algorithm [PDF]
, 2023 In 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 ...
Fink, Simon D., Rutter, Ignaz
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(Z)-3-[(3,5-Dichloroanilino)methylidene]-5-(4-methylphenyl)furan-2(3H)-one
IUCrData, 2018 The crystal structure of the title compound, C18H13Cl2NO2, at 120 K has triclinic (P\overline{1}) symmetry. The molecule demonstrates non-planarity in the solid state and a Z configuration for the exocyclic C=C bond.
Vyacheslav S. Grinev +2 more
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Extending Partial 1-Planar Drawings
CoRR, 2020 A shortened version of this article has been accepted for presentation and publication at the 47th International Colloquium on Automata, Languages and Programming (ICALP 2020)
Eduard Eiben +4 more
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Acta Crystallographica Section E, 2009 The title compound, C36H36N4O4, was prepared as a spirolactam ring formation of the rhodamine dye for comparison with a ring-opened form. The xanthene ring system is approximately planar [r.m.s.
Zhi-Hong Xu +3 more
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4-Amino-13-(1-naphthyl)-[2,2]paracyclophane
Acta Crystallographica Section E, 2008 The title compound [systematic name: 12-amino-42-(1-naphthyl)-1,4(1,4)-dibenzenacyclohexaphane], C26H23N, was synthesized from 4-amino-13-bromo-[2,2]paracyclophane and 1-naphthaleneboronic acid in the presence of 1,4-dioxane.
Yudao Ma +4 more
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(5Z,7Z)-6,8-Dimethyl-9H-tetrazolo[1,5-b][1,2,4]triazepine
Acta Crystallographica Section E, 2009 The molecule of the title compound, C6H8N6, is approximately planar, with a maximum deviation from planarity of 0.099 (1) Å.
Chun-Lin He +4 more
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IUCrData, 2016 The title compound, C8H4INO2, has a single planar molecule in the asymmetric unit, with the non-H atoms possessing a mean deviation from planarity of 0.058 Å. The molecules dimerize in the solid state through N—H...O hydrogen bonds.
James A. Golen, David R. Manke
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