The unavoidable arrangements of pseudocircles
نویسندگان
چکیده
منابع مشابه
Arrangements of Pseudocircles: On Circularizability
An arrangement of pseudocircles is a collection of simple closed curves on the sphere or in the plane such that every pair is either disjoint or intersects in exactly two crossing points. We call an arrangement intersecting if every pair of pseudocircles intersects twice. An arrangement is circularizable if there is a combinatorially equivalent arrangement of circles. Kang and Müller showed tha...
متن کاملArrangements of Arcs and Pseudocircles
Arrangements of (pseudo-)circles have already been studied in connection with algorithms in computational geometry. Thereby information on the numbers v k of intersection points contained in k circles seems to be particularly interesting. On each circle, there is an induced arrangement of arcs. This is why we begin by studying arrangements of arcs, and we arrive at a complete characterization o...
متن کاملArrangements of pseudocircles on surfaces
A pseudocircle is a simple closed curve on some surface. Arrangements of pseudocircles were introduced by Grünbaum, who defined them as collections of pseudocircles that pairwise intersect in exactly two points, at which they cross. There are several variations on this notion in the literature, one of which requires that no three pseudocircles have a point in common. Working under this definiti...
متن کاملArrangements 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 کاملForcing subarrangements in complete arrangements of pseudocircles
In arrangements of pseudocircles (i.e., Jordan curves) the weight of a vertex (i.e., an intersection point) is the number of pseudocircles that contain the vertex in its interior. We show that in complete arrangements (in which each two pseudocircles intersect) 2n−1 vertices of weight 0 force an α-subarrangement, a certain arrangement of three pseudocircles. Similarly, 4n−5 vertices of weight 0...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2019
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/14450