ISQED continues to provide and foster a unique opportunity to participants to interact and engage themselves in cutting edge tutorials, presentations, and panel and plenary sessions. The conference topics provide a holistic approach while covering a wide variety of issues impacting the quality of electronic design. We thank you for your support and anticipate your continued participation throug...

This paper contains a survey of different methods for generating knots and links based on geometric polyhedra, suitable for applications in chemistry, biology, architecture, sculpture (or jewelry). We describe several ways of obtaining 4-valent polyhedral graphs and their corresponding knots and links from geometrical polyhedra: midedge construction, cross-curve and double-line covering, and ed...

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...

‎let $g$ be a graph and $chi^{prime}_{aa}(g)$ denotes the minimum number of colors required for an‎ ‎acyclic edge coloring of $g$ in which no two adjacent vertices are incident to edges colored with the same set of colors‎. ‎we prove a general bound for $chi^{prime}_{aa}(gsquare h)$ for any two graphs $g$ and $h$‎. ‎we also determine‎ ‎exact value of this parameter for the cartesian product of ...

Given n points in the plane, a covering tree is a tree whose edges are line segments that jointly cover all the points. Let Gn be a n× · · · × n grid in Z. It is known that Gn can be covered by an axis-aligned polygonal path with 32n 2 + O(n) edges, thus in particular by a polygonal tree with that many edges. Here we show that every covering tree for the n points of Gn has at least (1 + c3)n 2 ...

The problem of packing Hamilton cycles in random and pseudorandom graphs has been studied extensively. In this paper, we look at the dual question of covering all edges of a graph by Hamilton cycles and prove that if a graph with maximum degree ∆ satisfies some basic expansion properties and contains a family of (1−o(1))∆/2 edge disjoint Hamilton cycles, then there also exists a covering of its...

Based on the most recent QSO ultraviolet spectra, the covering factor of the clouds of the Broad Line Region (BLR) is about 30%, or larger. This value would imply that in at least 30% of the QSOs our line of sight crosses one, or more, BLR clouds and, in the latter case, the UV spectrum should show a sharp Ly-edge in absorption. This Ly-edge in absorption is never observed. This paradox is solv...

abstract one of the basic assumptions in hub covering problems is considering the covering radius as an exogenous parameter which cannot be controlled by the decision maker. practically and in many real world cases with a negligible increase in costs, to increase the covering radii, it is possible to save the costs of establishing additional hub nodes. change in problem parameters during the pl...

A binary clutter is cycling if its packing and covering linear program have integral optimal solutions for all Eulerian edge capacities. We prove that the clutter of odd stwalks of a signed graph is cycling if and only if it does not contain as a minor the clutter of odd circuits of K5 nor the clutter of lines of the Fano matroid. Corollaries of this result include, of many, the characterizatio...

The Covering Steiner problem is a common generalization of the k-MST and Group Steiner problems. An instance of the Covering Steiner problem consists of an undirected graph with edge-costs, and some subsets of vertices called groups, with each group being equipped with a non-negative integer value (called its requirement); the problem is to find a minimum-cost tree which spans at least the requ...