Let G be a t uniform s regular linear hypergraph with r vertices It is shown that the number of independent sets I G in G satis es log I G r t O log ts s This leads to an improvement of a previous bound by Alon obtained for t i e for regular ordinary graphs It is also shown that for the Hamming graph H n q with vertices consisting of all n tuples over an alphabet of size q and edges connecting ...

Lovász conjectured that every connected 4-regular planar graph G admits a realization as a system of circles, i.e., it can be drawn on the plane utilizing a set of circles, such that the vertices of G correspond to the intersection and touching points of the circles and the edges of G are the arc segments among pairs of intersection and touching points of the circles. In this paper, we settle t...

A Digital Elevation Model (DEM) refers to a quantitative model of a part of the earth’s surface in digital form (Burrough and McDonnell, 1998). A DEM consists of either (1) a twodimensional array of numbers that represents the spatial distribution of elevations on a regular grid; (2) a set of x, y, and z coordinates for an irregular network of points; or (3) contour strings stored in the form o...

Semantic taxonomies such as WordNet provide a rich source of knowledge for natural language processing applications, but are expensive to build, maintain, and extend. Motivated by the problem of automatically constructing and extending such taxonomies, in this paper we present a new algorithm for automatically learning hypernym (is-a) relations from text. Our method generalizes earlier work tha...

A colouring of a strongly regular graph is an allocation of colours (or treatments) to the vertices of the graph. Such a colouring is balanced if every pair of distinct colours occurs equally often on the ends of an edge. When the graph is the complete regular multipartite graph a balanced colouring is just a balanced incomplete-block design, or 2-design. Some constructions are given. For examp...

The quadtree and the bintree data structures are two variants on the principle of hierarchical regular decomposition applied to image representation. A comparison of the storage requirements for images represented by these two methods is presented. The relative storage efficiency of quadand bintrees is determined by two factors: the relative node sizes for the two representations as determined ...