منابع مشابه
Arrangements of Pseudocircles and Circles
An arrangement of pseudocircles is a finite collection of Jordan curves in the plane with the additional properties that (i) every two curves meet in at most two points; and (ii) if two curves meet in a point p, then they cross at p. We say that two arrangements C = (c1, . . . , cn) and D = (d1, . . . , dn) are equivalent if there is a homeomorphism φ of the plane onto itself such that φ[ci] = ...
متن کاملOn the Complexity of Arrangements of Circles in the Plane
Continuing and extending the analysis in a previous paper [9], we establish several combinatorial results on the complexity of arrangements of circles in the plane. The main results are a collection of partial solutions to the conjecture that (a) any arrangement of unit circles with at least one intersecting pair has a vertex incident to at most 3 circles, and (b) any arrangement of circles of ...
متن کاملOn the Complexity of Many Faces in Arrangements of Circles
We obtain improved bounds on the complexity of m distinct faces in an arrangement of n circles and in an arrangement of n unit circles. The bounds are worst-case tight for unit circles, and, for general circles, they nearly coincide with the best known bounds for the number of incidences between m points and n circles.
متن کاملQuaternionic Product of Circles and Cycles and Octonionic Product for Pairs of Circles
This paper concerns with a product of circles induced by the quaternionic product considered in a projective manner. Several properties of this composition law are derived and on this way we arrive at some special numbers as roots or powers of unit. We extend this product to cycles as oriented circles and to pairs of circles by using the algebra of octonions. Three applications of the given pro...
متن کاملOn the Complexity of Many Faces in Arrangements of Pseudo-Segments and of Circles
We obtain improved bounds on the complexity of m distinct faces in an arrangement of n pseudo-segments, n circles, or n unit circles. The bounds are worst-case optimal for unit circles; they are also worst-case optimal for the case of pseudo-segments, except when the number of faces is very small, in which case our upper bound is a polylogarithmic factor from the best-known lower bound. For gen...
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ژورنال
عنوان ژورنال: Nexus Network Journal
سال: 2001
ISSN: 1590-5896,1522-4600
DOI: 10.1007/s00004-001-0026-5