منابع مشابه
Characterizing Certain Staircase Convex Sets in R
Let C = {C1, . . . , Cn} be a family of distinct boxes in R whose intersection graph is a tree, and let S = C1∪· · ·∪Cn. Let T ⊆ S. The set T lies in a staircase convex subset of S if and only if for every a, b in T there is an a−b staircase path in S. This result, in turn, yields necessary and sufficient conditions for S to be a union of k staircase convex sets, k ≥ 1. Analogous results charac...
متن کاملConnected Dominating Sets
PROBLEM DEFINITION Consider a graph G = (V,E). A subset C of V is called a dominating set if every vertex is either in C or adjacent to a vertex in C. If, furthermore, the subgraph induced by C is connected, then C is called a connected dominating set. A connected dominating set with a minimum cardinality is called a minimum connected dominating set (MCDS). Computing a MCDS is an NP-hard proble...
متن کاملDefinably connected nonconnected sets
We give an example of a structure K on the real line, and a manifold M definable in K, such that M is definably connected but is not connected.
متن کاملConnected Dominating Sets
Wireless sensor networks (WSNs), consist of small nodes with sensing, computation, and wireless communications capabilities, are now widely used in many applications, including environment and habitat monitoring, traffic control, and etc. Routing in WSNs is very challenging due to the inherent characteristics that distinguish these networks from other wireless networks like mobile ad hoc networ...
متن کاملSome Remarks on Connected Sets
This note will consist of a few disconnected remarks on connected sets . i. Swingle2 raised the question whether the plane is the sum of c disjoint biconnected sets . The answer as we shall show is affirmative . First we construct a biconnected set A with a dispersion point x such that any two points of A -x can be separated . (The first such set was constructed by Wilder.-' Our construction wi...
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 & Computational Geometry
سال: 2007
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-007-1308-9