Individual copy price: £5 The Centre for the Economics of Education is an independent research centre funded by the Department for Education and Skills. The views expressed in this work are those of the authors and do not necessarily reflect the views of the DfES. All errors and omissions remain the authors. Executive Summary Area-targeted regeneration policy implicitly assumes that neighbourho...

Given a positive integer n we find a graph G = (V,E) on |V | = n vertices with a minimum number of edges such that for any pair of non adjacent vertices x, y the graph G − x − y contains a (almost) perfect matching M . Intuitively the non edge xy and M form a (almost) perfect matching of G. Similarly we determine a graph G = (V,E) with a minimum number of edges such that for any matching M̄ of t...

The pebbling number of a graph G, f(G), is the least m such that, however m pebbles are placed on the vertices of G, we can move a pebble to any vertex by a sequence of moves, each move taking two pebbles o one vertex and placing one on an adjacent vertex. It is conjectured that for all graphs G and H , f(G H) f(G)f(H). Let Cm and Cn be cycles. We prove that f(Cm Cn) f(Cm)f(Cn) for all but a ni...

A proper edge colouring of a graph is neighbour-distinguishing if for all pairs of adjacent vertices v, w the set of colours appearing on the edges incident with v is not equal to the set of colours appearing on the edges incident with w. Let ndi(G) be the least number of colours required for a proper neighbour-distinguishing edge colouring of G. We prove that for d ≥ 4, a random d-regular grap...

Abstract This paper explores the relationship between quality of life and neighbourhood characteristics among immigrant local population in Storhaug (Stavanger) Grünerløkka (Oslo), two Norwegian neighbourhoods. The conditions have been analysed inhabitants interviewed to collect objective subjective data. Several dimensions considered, e.g., physical, environmental, mobility psychological, with...

OBJECTIVE Understanding the mechanisms by which neighbourhood environments influence childhood obesity is needed to facilitate the development of prevention strategies. The objective of this cross-sectional study was to identify the distinct types of neighbourhoods in which Canadian children reside and examine the extent to which physical activity and sedentary behaviour mediate the relationshi...

Multiple Knapsack Problem (MKP) is a most popular multiple subset selection problem that belongs to the class of NP-Complete problems. The aim is to assign optimal subsets among all original items to some knapsacks, such that the overall profit of all selected items be maximised, while the total weight of all assigned items to any knapsack does not exceed the allowable capacity of it. Artificia...

Three-neighbourhood Cellular Automata (CA) are widely studied and accepted as suitable cryptographic primitive. Rule 30, a 3-neighbourhood CA rule, was proposed as an ideal candidate for cryptographic primitive by Wolfram. However, rule 30 was shown to be weak against Meier-Staffelbach attack [7]. The cryptographic properties like diffusion and randomness increase with increase in neighbourhood...