Fast strategies in biased Maker--Breaker games
  We study the biased $(1:b)$ Maker--Breaker positional games, played on the edge set of the complete graph on $n$ vertices, $K_n$. Given Breaker's bias $b$, possibly depending on $n$, we determine the bounds for the minimal number of moves, depending on $b$, in which Maker can win in each of the two standard graph games, the Perfect Matching game and the Hamilton Cycle game. 
Mirjana Mikala\v{c}ki, Milo\v{s} Stojakovi\'c
math.CO