Geodesic
Fast strategies in biased Maker--Breaker games
Discrete mathematics & theoretical computer science, Tome 20 (2018) no. 2.

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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. 
@article{DMTCS_2018_20_2_a6,
     author = {Mikala\v{c}ki, Mirjana and Stojakovi\'c, Milo\v{s}},
     title = {Fast strategies in biased {Maker--Breaker} games},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2018},
     doi = {10.23638/DMTCS-20-2-6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-20-2-6/}
}
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Mikalački, Mirjana; Stojaković, Miloš. Fast strategies in biased Maker--Breaker games. Discrete mathematics & theoretical computer science, Tome 20 (2018) no. 2. doi : 10.23638/DMTCS-20-2-6. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-20-2-6/

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