A covering theorem about radial segments

A Covering Theorem with Applications

We prove a Covering Theorem that allows us to prove modified norm inequalities for general maximal operators. We will also give applications to convergence of a sequence of linear operators and the differentiation of the integral.

Covering Segments with Unit Squares

We study several variations of line segment covering problem with axis-parallel unit squares in IR. A set S of n line segments is given. The objective is to find the minimum number of axis-parallel unit squares which cover at least one end-point of each segment. The variations depend on the orientation and length of the input segments. We prove some of these problems to be NP-complete, and give...

Universal covering Maps and radial

Covering Salesman Problem with Nodes and Segments

In the Covering Salesman Problem (CSP), a distribution of nodes is provided, and the objective is to identify the shortest-length tour of a subset of all given nodes such that each node is not on the tour which is within a radius r of any node on the tour. In this paper, we define a new covering problem called the CSP with Nodes and Segments (CSPNS). The main difference between the CSP and the ...

On Leighton’s Graph Covering Theorem

We give short expositions of both Leighton’s proof and the BassKulkarni proof of Leighton’s graph covering theorem, in the context of colored graphs. We discuss a further generalization, needed elsewhere, to “symmetryrestricted graphs.” We can prove it in some cases, for example, if the “graph of colors” is a tree, but we do not know if it is true in general. We show that Bass’s Conjugation The...