On connected and regular point sets
نویسندگان
چکیده
منابع مشابه
Concerning Connected and Regular Point Sets
In this paper an extension will be given of a theorem of the author'sf which states that if A and B are any two points of a continuous curve M, and K denotes the set of all those points of M which separate} A and B in M, then K+A+B is a closed set of points. I t will be shown that if A and B are any two points of any connected and regular (connected im kleinen) point set M, and K denotes the se...
متن کاملConnected Rectilinear Graphs on Point Sets
Let V be a set of n points in R. We study the question whether there exists an orientation such that V is the vertex set of a connected rectilinear graph in that orientation. A graph is rectilinear if its edges are straight line segments in d pairwise perpendicular directions. We prove that at most one such orientation can be possible, up to trivial rotations of 90◦ around some axis. In additio...
متن کاملRegular and non-regular point sets: Properties and reconstruction
In this paper, we address the problem of curve and surface reconstruction from sets of points. We introduce regular interpolants, which are polygonal approximations of curves and surfaces satisfying a new regularity condition. This new condition, which is an extension of the popular notion of r-sampling to the practical case of discrete shapes, seems much more realistic than previously proposed...
متن کاملFour-connected triangulations of planar point sets
In this paper, we consider the problem of determining in polynomial time whether a given planar point set P of n points admits 4-connected triangulation. We propose a necessary and sufficient condition for recognizing P , and present an O(n) algorithm of constructing a 4-connected triangulation of P . Thus, our algorithm solves a longstanding open problem in computational geometry and geometric...
متن کاملFinding Independent Sets inK4-Free 4-Regular Connected Graphs
Let G be a K4-free 4-regular connected graph with & vertices. Then G contains an independent set of vertices of cardinality at least (7&&4) 26. Furthermore, the proof will yield a polynomial-time algorithm which will return an independent set of cardinality at least (7&&4) 26 for any such graph. A family of K4 -free 4-regular connected graphs with maximum independent set of cardinality 3 11& is...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1928
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1928-04647-5