Triangulations with many points of even degree
نویسندگان
چکیده
Let S be a set of points in the plane in general position. A triangulation of S will be called even if all the points of S have an even degree. We show how to construct a triangulation of S containing at least ⌊ 2n 3 ⌋−3 points with even degree; this improves slightly the bound of ⌈ 2(n−1) 3 ⌉ − 6 by Aichholzer et. al. [1]. Our proof can be easily adapted to give, through a long case analysis, triangulations with ⌊ 4n 5 ⌋ − c vertices with even degree.
منابع مشابه
Even Triangulations of Planar Set of Points with Steiner Points
Let P ⊂ R be a set of n points of which k are interior points. Let us call a triangulation T of P even if all its vertices have even degree, and pseudo-even if at least the k interior vertices have even degree. (Pseudo-) Even triangulations have one nice property; their vertices can be 3-colored, see [2, 3, 4]. Since one can easily check that for some sets of points, such triangulation do not e...
متن کاملParity-Constrained Triangulations with Steiner Points
Let P ⊂ R be a set of n points, of which k lie in the interior of the convex hull CH(P) of P . Let us call a triangulation T of P even (odd) if and only if all its vertices have even (odd) degree, and pseudo-even (pseudo-odd) if at least the k interior vertices have even (odd) degree. On the one hand, triangulations having all its interior vertices of even degree have one nice property; their v...
متن کاملParallel Enumeration of Triangulations
We report on the implementation of an algorithm for computing the set of all regular triangulations of finitely many points in Euclidean space. This algorithm, which we call down-flip reverse search, can be restricted, e.g., to computing full triangulations only; this case is particularly relevant for tropical geometry. Most importantly, down-flip reverse search allows for massive parallelizati...
متن کاملEnumerating Triangulations for Products of Two Simplices and for Arbitrary Configurations of Points
We propose algorithms to enumerate (1) classes of regular triangulations in respect of symmetry for products of two simplices and (2) all triangulations, regular or not, for arbitrary con gurations of points. There are many results for triangulations in two dimension, but little is known for higher dimensions. Both objects we enumerate in this paper are for general dimensions. Products of two s...
متن کاملN-flips in even triangulations on the sphere
A triangulation is said to be even if each vertex has even degree. For even triangulations, define the N -flip and the P2-flip as two deformations preserving the number of vertices. We shall prove that any two even triangulations on the sphere with the same number of vertices can be transformed into each other by a sequence of N and P2-flips.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010