منابع مشابه
On Obstacle Numbers
The obstacle number is a new graph parameter introduced by Alpert, Koch, and Laison (2010). Mukkamala et al. (2012) show that there exist graphs with n vertices having obstacle number in Ω(n/ log n). In this note, we up this lower bound to Ω(n/(log log n)2). Our proof makes use of an upper bound of Mukkamala et al. on the number of graphs having obstacle number at most h in such a way that any ...
متن کاملGraphs with Large Obstacle Numbers
Motivated by questions in computer vision and sensor networks, Alpert et al. [3] introduced the following definitions. Given a graph G, an obstacle representation of G is a set of points in the plane representing the vertices of G, together with a set of connected obstacles such that two vertices of G are joined by an edge if an only if the corresponding points can be connected by a segment whi...
متن کاملConvex obstacle numbers of outerplanar graphs and bipartite permutation graphs
The disjoint convex obstacle number of a graph G is the smallest number h such that there is a set of h pairwise disjoint convex polygons (obstacles) and a set of n points in the plane (corresponding to V (G)) so that a vertex pair uv is an edge if and only if the corresponding segment uv does not meet any obstacle. We show that the disjoint convex obstacle number of an outerplanar graph is alw...
متن کاملOn generalized fuzzy numbers
This paper first improves Chen and Hsieh’s definition of generalized fuzzy numbers, which makes it the generalization of definition of fuzzy numbers. Secondly, in terms of the generalized fuzzy numbers set, we introduce two different kinds of orders and arithmetic operations and metrics based on the λ-cutting sets or generalized λ-cutting sets, so that the generalized fuzzy numbers are integrat...
متن کاملToward Obstacle Avoidance on Quadrotors
OS4 (Omnidirectional Stationary Flying OUtstretched Robot) is an electrically powered four-rotor miniature helicopter developed towards fully autonomous operation in indoor/outdoor environments. The major goal of this research is the development and implementation of an active control system for a quadrotor helicopter. However, one has to consider seriously the design aspect in order to get rid...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2015
ISSN: 1077-8926
DOI: 10.37236/4373