Geodesic
Doubly biased Walker-Breaker games
Jovana Forcan1 ; Mirjana Mikalački1 ; Jovana Forcan ; Mirjana Mikalački
1Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Novi Sad, Serbia
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 685-688 
Jovana Forcan; Mirjana Mikalački; Jovana Forcan; Mirjana Mikalački. Doubly biased Walker-Breaker games. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 685-688. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a50/
@article{AMUC_2019_88_3_a50,
     author = {Jovana Forcan and Mirjana Mikala\v{c}ki and Jovana Forcan and Mirjana Mikala\v{c}ki},
     title = { Doubly biased {Walker-Breaker} games},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {685--688},
     year = {2019},
     volume = {88},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a50/}
}
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Voir la notice de l'article provenant de la source Comenius University

We study doubly biased Walker--Breaker games, played on the edge set of a complete graph on $n$ vertices, $K_n$. Walker--Breaker game is a variant of Maker--Breaker game, where Walker, playing the role of Maker, must choose her edges according to a walk, while Breaker has no restrictions on choosing his edges. Here we show that for $b\leq \frac{n}{10\ln{n}}$, playing a $(2:b)$ game on $E(K_n)$, Walker can create a graph containing a spanning tree. Also, we determine a constant $c > 0$ such that Walker has a strategy to make a Hamilton cycle of $K_n$ in the $(2 : \frac{cn}{\ln{n}})$ game.