For an arbitrary countable ordinal α, we construct a game in which weak and strong domination coincide, and in which α rounds of elimination of dominated strategies are required to solve a game.

One of the central assumptions of Optimality Theory is the hypothesis of strict domination among constraints. A few studies have suggested that this hypothesis is too strong and should be abandoned in favor of a weaker cumulativity hypothesis. If this suggestion is correct, we should be able to find evidence for cumulativity in the comprehension of Gapping sentences, which lack explicit syntact...

Who is in favour of domination? Surely some people have a strong interest in preserving it, but as this is not publicly confessable and people enjoy picturing themselves as moral, everyone will officially support a non-domination programme. What is more, Ian Shapiro suggests, in circumstances where ‘you cannot be confident of your ability to dominate others’, it is in your interest ‘to create a...

In this paper, the effect of the removal of a node or an arc of a fuzzy graph on the minimum strong dominating set of the fuzzy graph is studied. The motivation behind this study is the identification of fault tolerance in the topological design of a network. That is, the ability of the network to provide service even when it contains a faulty component or components. MSC: 05C69.

Let H be a 3-uniform hypergraph of order n and size m, and let T be a subset of vertices of H. The set T is a strong transversal in H if T contains at least two vertices from every edge of H. The strong transversal number τs(H) of H is the minimum size of a strong transversal in H. We show that 7τs(H) ≤ 4n+ 2m, and we characterize the hypergraphs that achieve equality in this bound. In particul...

For the classical Lp-spaces of signed measures on N, we devise a framework in which bounds for a sub-Markovian semigroup of interest can be obtained, up to a constant factor, from bounds for another tractable semigroup that dominates stochastically the first one. The main tools are the Hardy inequality, the definition of related auxiliary Lp spaces suited to take advantage of the domination, an...

A subset S of vertices in a graph G is called a geodetic set if every vertex not in S lies on a shortest path between two vertices from S. A subset D of vertices in G is called dominating set if every vertex not in D has at least one neighbor in D. A geodetic dominating set S is both a geodetic and a dominating set. The geodetic (domination, geodetic domination) number g(G)(γ(G), γg(G)) of G is...

For any edge of an isolate free graph , , 〈 〉 is the subgraph induced by the vertices adjacent to u and v in G. We say that an edge x, edominates an edge y if ∈ 〈 〉 . A set ⊆ is an Edge-Edge Dominating Set (EED-set) if every edge in is e-dominated by an edge in L. The edgeedge domination number is the cardinality of a minimum EED-set. We find the relation ship between the new parameter and some...