Showing papers on "Planarity testing published in 1984"
TL;DR: A simple linear-time algorithm that solves all three recognition problems and is previously used in general planarity testing, called a pile of twin stacks is described.
39 citations
TL;DR: Graph theory methods were used to analyze the topology of the renal glomerular capillary network using data both from a serial reconstruction of a rat glomerulus and from the literature, and a node degree distribution function estimate was obtained.
13 citations
8 citations
TL;DR: In this paper, a spectral estimator is constructed from only two starting requirements: closeness to an original autocorrelation estimate and planarity, i.e., smoothness, of the corresponding spectral estimators.
Abstract: An approach to spectral estimation is developed. The estimator is constructed from only two starting requirements: closeness to an original autocorrelation estimate and planarity, i.e., smoothness, of the corresponding spectral estimator. The inverse of the variance of the original autocorrelation estimate enters as a weight. By making various a priori assumptions about the variance, and by selecting two mathematical formulations of the planarity requirement, both the classical window and the maximum entropy methods result as special cases. Thus, the two methods are put together since they follow from the same starting requirements. Attention is given to the case where both the variance is estimated in terms of the original autocorrelation estimate, and planarity is forced by the minimization of a functional involving the absolute value of the power spectrum derivatives. A window method results but with a variance dependent window involving two parameters, the order of the derivative and a parameter equivalent to the window width. An application to a meteorological process is included as an illustration.
7 citations
TL;DR: In this paper, the authors report some theoretical calculations related to the conformation of 4−n alkyl−4′−cyanobiphenyls (n ≥ 6) performed by means of a quantum mechanical approach and classical electrostatic chemical bond method.
Abstract: We report some theoretical calculations related to the conformation of 4‐n alkyl‐4′‐cyanobiphenyls (n≤6), performed by means of a quantum mechanical approach and classical electrostatic chemical bond method. The main results of this study are (i) the planarity of the cyanobiphenyl skeleton, and (ii) a strong intramolecular perturbation of the conformational order of the alkyl tail were trans form is largely favored. Such a perturbation is expected to vanish for n≥6.
7 citations
01 Jan 1984
TL;DR: In this article, a mining project where four substances sand, turf, coal, and earth are being extracted at five different sources is considered, and four locations where the different materials will be collected, labelled S, T, C, and E respectively.
Abstract: Consider a mining project where four substances sand, turf, coal, and earth are being extracted at five different sources. One also has four locations where the different materials will be collected, labelled S, T, C, and E respectively.
6 citations
TL;DR: It is proved that any non-planar 3-connected graph with at least 6 vertices contains a cycle with three pairwise ‘interwoven’ chords.
6 citations
TL;DR: This paper presents a simple linear algorithm based on the “vertex-addition algorithm” of Lempel, Even and Cederbaum for planarity testing and is a slight modification of Booth and Lueker's implementation of the testing algorithm using a PQ-tree.
Abstract: The problems of testing the planarity of a graph and of embedding a planar graph in a plane arise in many applications. This paper presents a simple linear algorithm for the latter problem. the algorithm is based on the “vertex-addition algorithm” of Lempel, Even and Cederbaum for planarity testing and is a slight modification of Booth and Lueker's implementation of the testing algorithm using a PQ-tree. Compared with the embedding algorithm known as the “path-addition” algorithm of Hopcroft and Tarjan, our algorithm is conceptually simple and easy to understand or implement.
3 citations
2 citations
TL;DR: The crystal structure of 2-dimethylaminobenzenediazonium tetrafluoroborate has been determined at 183 K by X-ray diffraction.
Abstract: The crystal structure of 2-dimethylaminobenzenediazonium tetrafluoroborate has been determined at 183 K by X-ray diffraction. The cation is very nearly planar, the strong steric interaction between the ortho-groups being diminished by in-plane angular distoritions.