Cycle covering is a well-studied problem in computer science. In this paper, we develop approximation algorithms for variants of cycle covering problems which bound the size and/or length of the covering cycles. In particular, we give a (1 + ln 2)-approximation for the lane covering problem [4, 5] in weighted graphs with metric lengths on the edges and an O(ln k) approximation for the bounded c...

We study the problem of designing a survivable WDM network based on covering the communication requests with subnetworks that are protected independently from each other. We consider here the case when the physical network is T (n), a torus of size n by n, the subnetworks are cycles and the communication scheme is all-to-all or total exchange (where all pairs of vertices communicate). We will r...

We measure the frequency dependent capacitance of a gate covering the edge and part of a 2D electron gas in the quantum Hall regime. In applying a positive gate bias, we create a metallic “puddle” under the gate surrounded by an insulating region. This puddle charges via electron tunneling from an edge channel. The determined tunneling conductance displays novel resonances as a function of gate...

Given a planar straight line graph we seek a covering triangulation whose minimumangle is as large as possible A covering triangulation is a Steiner triangulation with the following restriction No Steiner vertices may be added on an input edge We give an explicit upper bound on the largest possible minimum angle in any covering triangulation of a given input This upper bound depends only on loc...

Song, Havlin and Makse (2005) have recently used a version of the box-counting method, called the node-covering method, to quantify the self-similar properties of 43 cellular networks: the minimal number NV of boxes of size l needed to cover all the nodes of a cellular network was found to scale as the power law NV ∼ (l+1) −DV with a fractal dimension DV = 3.53±0.26. We propose a new box-counti...

This paper considers the cycle covering of complete graphs motivated by the design of survivable WDM networks, where the requests are routed on sub-networks which are protected independently from each other. The problem can be stated as follows : for a given graph G, find a cycle covering of the edge set of Kn, where V (Kn) = V (G), such that each cycle in the covering satisfies the disjoint ro...

let $g=(v‎, ‎e)$ be a graph with $p$ vertices and $q$ edges‎. ‎an emph{acyclic‎ ‎graphoidal cover} of $g$ is a collection $psi$ of paths in $g$‎ ‎which are internally-disjoint and cover each edge of the graph‎ ‎exactly once‎. ‎let $f‎: ‎vrightarrow {1‎, ‎2‎, ‎ldots‎, ‎p}$ be a bijective‎ ‎labeling of the vertices of $g$‎. ‎let $uparrow!g_f$ be the‎ ‎directed graph obtained by orienting the...

A simple graph G = (V (G), E(G)) admits an H-covering, if every edge in E(G) belongs to at least one subgraph of G isomorphic to a given graph H. An (a, d)-H-antimagic total labeling of G admitting an H-covering is a bijective function ξ : V (G) ∪ E(G) → {1, 2, . . . , |V (G)| + |E(G)|} such that for all subgraphs H ′ isomorphic to H, the H-weights w(H ′) = ∑

We consider definably compact groups in an o-minimal expansion of a real closed field. It is known that to each such group G is associated a natural exact sequence 1→ G00 → G → G/G00 → 1 where G00 is the “infinitesimal subgroup” of G and G/G00 is a compact real Lie group. We show that given a connected open subset U of G/G00 there is a canonical isomorphism between the fundamental group of U an...

In this paper we fix 7 types of undirected graphs: paths, paths with prescribed endvertices, circuits, forests, spanning trees, (not necessarily spanning) trees and cuts. Given an undirected graph G = (V, E) and two “object types” A and B chosen from the alternatives above, we consider the following questions. Packing problem: can we find an object of type A and one of type B in the edge set E ...