We study biased Maker/Breaker games on the edges of the complete graph, as introduced by Chvátal and Erdős. We show that Maker, occupying one edge in each of his turns, can build a spanning tree, even if Breaker occupies b ≤ (1 − o(1)) · n lnn edges in each turn. This improves a result of Beck, and is asymptotically best possible as witnessed by the Breaker-strategy of Chvátal and Erdős. We als...

Circuit Breaker is one of the most critical elements of power industry. Controlled Switching of grid voltage and grid current is the best solution to prevent the high inrush current and over voltages. This paper describes the Controlled Switching of Circuit Breaker by using multiprocessor based architecture. With this architecture early detection of most of major fault is feasible; it is also p...

We look at Maker-Breaker k-clique game played on the edge set of the random graph G(n, p). In this game, two players, Maker and Breaker, alternately claim unclaimed edges of G(n, p), until all the edges are claimed. Maker wins if he claims all the edges of a k-clique; Breaker wins otherwise. We determine that the property that Maker can win this game has a threshold at n− 2 k+1 , for all k > 3....

We study Maker/Breaker games on the edges of sparse graphs. Maker and Breaker take turns in claiming previously unclaimed edges of a given graph H . Maker aims to occupy a given target graph G and Breaker tries to prevent Maker from achieving his goal. We define a function f on the integers and show that for every d-regular graph G on n vertices there is a graph H with at most f(d)n edges such ...

Two new versions of the so-called Maker-Breaker Positional Games are defined by József Beck. In these variants Picker takes unselected pair of elements and Chooser keeps one of these elements and gives back the other to Picker. In the Picker-Chooser version Picker is Maker and Chooser is Breaker, while the roles are swapped in the Chooser-Picker version. It seems that both the Picker-Chooser an...

The high amplitude and steep overvoltage generated by the breaking of vacuum circuit breaker in wind farm damages inter-turn insulation transformer. There is a certain difference between simulation results traditional reignition model measured overvoltage. It necessary to improve simulate condition transformer more accurately then select appropriate protection measures. In this paper, based on ...

The above is called the “strong” version of the game. In the “weak” version, also called “maker-breaker”, the second player’s aim is not to occupy a winning set but just to prevent the first player from doing so. The interest is both for general theorems about games and also in particular games of interest, like the Hales-Jewett game (multi-dimensional noughts & crosses). Roughly speaking, a fa...