Uniqueness of maximum planar five-distance sets
نویسندگان
چکیده
منابع مشابه
Distance Sets of Well-distributed Planar Sets for Polygonal Norms
Let X be a 2-dimensional normed space, and let BX be the unit ball in X. We discuss the question of how large the set of extremal points of BX may be if X contains a well-distributed set whose distance set ∆ satisfies the estimate |∆ ∩ [0, N ]| ≤ CN3/2− . We also give a necessary and sufficient condition for the existence of a well-distributed set with |∆ ∩ [0, N ]| ≤ CN .
متن کاملDistance Sets of Well-Distributed Planar Point Sets
We prove that a well-distributed subset of R2 can have a distance set ∆ with #(∆ ∩ [0, N ]) ≤ CN3/2− only if the distance is induced by a polygon K. Furthermore, if the above estimate holds with = 1/2, then K can have only finitely many sides.
متن کاملDifferent-Distance Sets in a Graph
A set of vertices $S$ in a connected graph $G$ is a different-distance set if, for any vertex $w$ outside $S$, no two vertices in $S$ have the same distance to $w$.The lower and upper different-distance number of a graph are the order of a smallest, respectively largest, maximal different-distance set.We prove that a different-distance set induces either a special type of path or an independent...
متن کاملQuadrangulations of Planar Sets
A linear-time algorithm for decomposing recti-linear star-shaped polygons into convex quadrilaterals, " Proc.
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: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.08.028