Domination game is a played on finite, undirected graph G, between two players Dominator and Staller. During the game, alternately choose vertices of G such that each chosen vertex dominates at least one new not dominated by previously vertices. The aim to finish as early possible while Staller delay process much possible. domination number γg(G) total moves in when starts both play optimally. ...

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...

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 ...

A k-dominating set of a graph G is a set S of vertices of G such that every vertex outside of S has k neighbors in S. The k-domination number of G, written γk(G), is the size of the smallest k-dominating set in G. In this paper, we derive sharp upper and lower bounds on γk(G) + γk(G) and γk(G)γk(G), where G is the complement of G. We use the results for k = 2 to prove a conjecture of Alon, Balo...