The large volume of intra-industry trade is often cited as a critical element favoring trade theories based on increasing returns and imperfect competition over those with constant returns and perfect competition. The former provide an elegant account of intra-industry trade, while the latter, it is often argued, cannot. This paper provides an account of intra-industry trade based squarely on c...

A graph is k-domination-critical if γ(G)=k, and for any edge e not in G, γ(G+e) = k-1. In this paper we show that the diameter of a domination k-critical graph with k≥2 is at most 2k-2. We also show that for every k≥2, there is a k-domination-critical graph having diameter 3 2 k 1 −     . We also show that the diameter of a 4-domination-critical graph is at most 5.

In this paper Gallai’s inequality on the number of edges in critical graphs is generalized for reducible additive induced-hereditary properties of graphs in the following way. Let P1,P2, . . . ,Pk (k ≥ 2) be additive induced-hereditary properties, R = P1◦ P2◦ · · · ◦Pk and δ = ∑k i=1 δ(Pi). Suppose that G is an R-critical graph with n vertices and m edges. Then 2m ≥ δn + δ−2 δ2+2δ−2 n + 2δ δ2+2...

Few things are as fundamental to the human experience as the interaction between humans and their environment—be it physical or virtual. A critical element of this interaction involves movement through space. We know that what we often refer to as navigation is not merely physical translation through a space, termed locomotion or travel, but that there is also a cognitive element, often referre...

A graph G is domination dot-critical, or just dot-critical, if contracting any edge decreases the domination number. It is totally dot-critical if identifying any twovertices decreases the domination number. In this paper, we study an open question concerning of the diameter of a domination dot-critical graph G. © 2008 Elsevier B.V. All rights reserved.

A critical element in the sustainability of any public policy is the fair treatment of ‘similar’ individuals. This paper introduces a new dimension of merit to evaluate public school assignment mechanisms based on this notion of horizontal equity. The findings reveal that all of the prominent assignment mechanisms discussed in the literature fail to satisfy this ‘equal treatment’ criterion. I a...

In a graph a vertex is said to dominate itself and all its neighbors. A double dominating set of a graph G is a subset of vertices that dominates every vertex of G at least twice. The double domination number of G, denoted γ×2(G), is the minimum cardinality among all double dominating sets ofG. We consider the effects of vertex removal on the double domination number of a graph. A graph G is γ×...

A locating-dominating set D of a graph G = (V (G), E(G)) is a set D ⊆ V (G) such that every vertex of V (G) − D is adjacent to a vertex of D and for every pair of distinct vertices u, v in V (G) − D, N(u) ∩ D = N(v) ∩ D. The minimum cardinality of a locating-dominating set is denoted by γL(G). A graph G is said to be a locating domination edge removal critical graph, or just γ L -ER-critical gr...

Let G be a connected graph. The core of G, denoted by G∆, is the subgraph of G induced by the vertices of maximum degree. Hilton and Zhao [On the edge-colouring of graphs whose core has maximum degree two, JCMCC 21 (1996), 97-108] conjectured that, if ∆(G∆) ≤ 2, then G is Class 2 if and only if G is overfull, with the sole exception of the Petersen graph with one vertex deleted. In this paper w...