The connected domination game is played just as the game, with an additional requirement that at each stage of vertices induce a subgraph. number moves in D-game (an S-game, resp.) on graph G when both players play optimally denoted by $$\gamma _\mathrm{cg}(G)$$ ( _\mathrm{cg}'(G)$$ , resp.). Connected Game Continuation Principle established substitute for classical which does not hold game. Le...

Assume we have a set of k colors and to each vertex of a graph G we assign an arbitrary subset of these colors. If we require that each vertex to which an empty set is assigned has in its neighborhood all k colors, then this is called the k-rainbow dominating function of a graph G. The corresponding invariant γrk(G), which is the minimum sum of numbers of assigned colors over all vertices of G,...

by Dune Nixon : '"The Albany State booters broke their three game'losing streak Saturday with a decisive 4-1 win over Brooklyn College. The Great Danes, led by high-scoring Maurice Tsododo, really seemed to jell in this one. All phases of their game came around at once and resulted in an almost complete domination of the Brooklyn eleven. As the game got under way it looked as if Albany might be...

In this Note, assuming that the generator is uniform Lipschitz in the unknown variables, we relate the solution of a one dimensional backward stochastic differential equation with the value process of a stochastic differential game. Under a domination condition, an Fconsistent evaluations is also related to a stochastic differential game. This relation comes out of a min-max representation for ...