A two person (or bimatrix) game is a pair of m x n matrices A. B, with integer entries. This game is played between two players A and B. Player A chooses a row t. player B simultaneously chooses a column j. As a result. A receives a,, (dollars, say), and B receives b,,. An easy way to simplify a bimatrix game is to eliminate from both A and B any strategy (row or column) that is dominated by an...

We present an algorithm which determines the outcome of an arbitrary Hex game-state by finding a winning virtual connection for the winning player. Our algorithm performs a recursive descent search of the game-tree, combining fixed and dynamic game-state virtual connection composition rules with some new Hex game-state reduction results based on move domination. The algorithm is powerful enough...

We present an algorithm which determines the outcome of an arbitrary Hex game-state by finding a winning virtual connection for the winning player. Our algorithm performs a recursive descent search of the game-tree, combining fixed and dynamic game-state virtual connection composition rules with some new Hex game-state reduction results based on move domination. The algorithm is powerful enough...

We study Maker--Breaker total domination game played by two players, Dominator and Staller, on the connected cubic graphs. Staller (playing role of Maker) wins if she manages to claim an open neighbourhood a vertex. otherwise (i.e.\ he can dominating set graph). For certain graphs $n\geq 6$ vertices, we give characterization those which are Dominator's win Staller's win.

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. ...