Chromatic Properties of Generic Planar Configurations of Points
نویسندگان
چکیده
We study the Orchard relation defined in [3] for generic configurations of points in the plane (also called order types). We introduce infinitesimally-close points and analyse the relation of this notion with the Orchard relation. The second part of the paper deals with monochromatic configurations (for the Orchard relation). We give the complete list of all monochromatic configurations up to 7 points and present some constructions and families of monochromatic configurations.
منابع مشابه
Capturing Outlines of Planar Generic Images by Simultaneous Curve Fitting and Sub-division
In this paper, a new technique has been designed to capture the outline of 2D shapes using cubic B´ezier curves. The proposed technique avoids the traditional method of optimizing the global squared fitting error and emphasizes the local control of data points. A maximum error has been determined to preserve the absolute fitting error less than a criterion and it administers the process of curv...
متن کاملThe Number of Planar Central Configurations Is Finite When N − 1 Mass Positions Are Fixed
In this paper, it is proved that for n > 2 and n 6= 4, if n−1 masses are located at fixed points in a plane, then there are only a finite number of n-point central configurations that can be generated by positioning a given additional nth mass in the same plane. The result is established by proving an equivalent isolation result for planar central configurations of five or more points. Other ge...
متن کاملVisible Lattice Points and the Chromatic Zeta Function of a Graph
We study the probability that a random polygon of k vertices in the lattice {1, . . . , n}s does not contain more lattice points than the k vertices of the polygon. Then we introduce the chromatic zeta function of a graph to generalize this problem to other configurations induced by a given graph H.
متن کاملThe chromatic number of the square of subcubic planar graphs
Wegner conjectured in 1977 that the square of every planar graph with maximum degree at most 3 is 7-colorable. We prove this conjecture using the discharging method and computational techniques to verify reducible configurations. Mathematics Subject Classification: Primary 05C15; Secondary 05C10, 68R10.
متن کاملA Computational Study to Find the Vibrational Modes Connected with Specific Molecular Structures of Calculated Compound
The purpose of this research is to provide a deeper understanding of the planar high- symmetry configuration instability. In the ideal case, the distortion corresponds to the movements of nuclei along normal modes that belong to non-totally symmetric irreps of the high symmertry (HS) point group of molecule. The analysis of the structural distortion from the HS nuclear arrangements of the JT ac...
متن کامل