A graph G is given and two players, a cop and a robber, play the folioking game: the cop chooses a vertex, then the robber chooses a vertex, then the players move alternately beginning with the cop. A move consists of staying at one’s present vertex or moving to an adjacent vertex; each move is seen by both players. The cop wins if he manages to occupy the same vertex as the robber, and the rob...

The disciplines of town planning and public health have investigated the connection between walking and neighbourhood form (e.g., Frank et al. 2003; Frumkin et al., 2004). In particular, Terri Pikora and her colleagues (2003) created a schema to classify a range of potential elements that may influence an adult’s decision to walk. By reviewing the health, urban planning and transport-related li...

We investigate generalizations of pebbling numbers and of Graham’s pebbling conjecture that π(G × H) ≤ π(G)π(H), where π(G) is the pebbling number of the graph G. We develop new machinery to attack the conjecture, which is now twenty years old. We show that certain conjectures imply others that initially appear stronger. We also find counterexamples that show that Sjöstrand’s theorem on cover p...

Neighbourhood Effects Research at a Crossroads: Ten Challenges for Future Research Neighbourhood effects research is at a crossroads since current theoretical and empirical approaches do not seem to be moving the debate forward. In this paper, we present a set of ten challenges as a basis for a new research agenda which will give new direction to the neighbourhood effects debate. The ten challe...

Given a polygon P in the plane, a pop operation is the reflection of a vertex with respect to the line through its adjacent vertices. We define a family of alternating polygons, and show that any polygon from this family cannot be convexified by pop operations. This family contains simple, as well as non-simple (i.e., self-intersecting) polygons, as desired. We thereby answer in the negative an...

The pebbling number f(G) of a graphG is the least p such that, no matter how p 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 off one vertex and placing one on an adjacent vertex. It is conjectured that for all graphs G and H , we have f(G × H) ≤ f(G)f(H). If the graph G satisfies the odd 2-pebbling property, we w...

This paper explores a new language of neighbourhood structures where existential information can be given about what kind of worlds occur in a neighbourhood of a current world. The resulting system of ‘instantial neighbourhood logic’ INL has a non-trivial mix of features from relational semantics and from neighbourhood semantics. We explore some basic model-theoretic behavior, including a match...

APrIl 2017 IZA DP No. 10694 Incorporating Neighbourhood Choice in a Model of Neighbourhood Effects on Income Studies of neighbourhood effects often attempt to identify causal effects of neighbourhood characteristics on individual outcomes, such as income, education, employment, and health. However, selection looms large in this line of research and it has been repeatedly argued that estimates o...