منابع مشابه
Distance Coloring of the Hexagonal Lattice
Motivated by the frequency assignment problem we study the ddistant coloring of the vertices of an infinite plane hexagonal lattice H. Let d be a positive integer. A d-distant coloring of the lattice H is a coloring of the vertices of H such that each pair of vertices distance at most d apart have different colors. The d-distant chromatic number of H, denoted χd(H), is the minimum number of col...
متن کاملDistance Coloring
Given a graphG = (V,E), a (d, k)-coloring is a function from the vertices V to colors {1, 2, . . . , k} such that any two vertices within distance d of each other are assigned different colors. We determine the complexity of the (d, k)-coloring problem for all d and k, and enumerate some interesting properties of (d, k)-colorable graphs. Our main result is the discovery of a dichotomy between p...
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In this paper, a new structure is provided for the dispersion compensating photonic crystal fibers in order to broaden the chromatic dispersion and increase the dispersion compensating capability in a wide wavelength range. In the structure, putting elliptical holes in the first ring of the inner core clad of a dispersion compensating fiber of the hexagonal lattice, increases the wavelength ran...
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How many sublattices of index N are there in the planar hexagonal lattice? Which of them are the best from the point of view of packing density, signal-to-noise ratio, or energy? We answer the first question completely and give partial answers to the other questions.
متن کاملThe hexagonal versus the square lattice
Schmutz Schaller’s conjecture regarding the lengths of the hexagonal versus the lengths of the square lattice is shown to be true. The proof makes use of results from (computational) prime number theory. Using an identity due to Selberg, it is shown that, in principle, the conjecture can be resolved without using computational prime number theory. By our approach, however, this would require a ...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2005
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.1269