7 research outputs found
Spanning tree game as prim would have played
In this paper, we investigate special types of Maker-Breaker games defined on graphs. We restrict Maker’s possible moves that resembles the way that was introduced by Espig, Frieze, Krivelevich and Pedgen [9]. Here, we require that the subgraph induced by Maker’s edges must be connected throughout the game. Besides the normal play, we examine the biased and accelerated versions of these games
Walker-Breaker Games on
The Maker-Breaker connectivity game and Hamilton cycle game belong to the
best studied games in positional games theory, including results on biased
games, games on random graphs and fast winning strategies. Recently, the
Connector-Breaker game variant, in which Connector has to claim edges such that
her graph stays connected throughout the game, as well as the Walker-Breaker
game variant, in which Walker has to claim her edges according to a walk, have
received growing attention.
For instance, London and Pluh\'ar studied the threshold bias for the
Connector-Breaker connectivity game on a complete graph , and showed that
there is a big difference between the cases when Maker's bias equals or
. Moreover, a recent result by the first and third author as well as Kirsch
shows that the threshold probability for the Connector-Breaker
connectivity game on a random graph is of order
. We extent this result further to Walker-Breaker games and
prove that this probability is also enough for Walker to create a Hamilton
cycle