TY - JOUR
T1 - Fast embedding of spanning trees in biased Maker-Breaker games
AU - Ferber, Asaf
AU - Hefetz, Dan
AU - Krivelevich, Michael
N1 - Funding Information:
This research was supported in part by USA–Israel BSF Grant 2006322 and by grant 1063/08 from the Israel Science Foundation .
PY - 2012/8
Y1 - 2012/8
N2 - Given a tree T=(V, E) on n vertices, we consider the (1:q) Maker-Breaker tree embedding game T n. The board of this game is the edge set of the complete graph on n vertices. Maker wins Tn if and only if she is able to claim all edges of a copy of T. We prove that there exist real numbers α, ε>0 such that, for sufficiently large n and for every tree T on n vertices with maximum degree at most n ε, Maker has a winning strategy for the (1:q) game Tn, for every q≤n α. Moreover, we prove that Maker can win this game within n+o(n) moves which is clearly asymptotically optimal.
AB - Given a tree T=(V, E) on n vertices, we consider the (1:q) Maker-Breaker tree embedding game T n. The board of this game is the edge set of the complete graph on n vertices. Maker wins Tn if and only if she is able to claim all edges of a copy of T. We prove that there exist real numbers α, ε>0 such that, for sufficiently large n and for every tree T on n vertices with maximum degree at most n ε, Maker has a winning strategy for the (1:q) game Tn, for every q≤n α. Moreover, we prove that Maker can win this game within n+o(n) moves which is clearly asymptotically optimal.
UR - http://www.scopus.com/inward/record.url?scp=84857025656&partnerID=8YFLogxK
U2 - 10.1016/j.ejc.2012.01.007
DO - 10.1016/j.ejc.2012.01.007
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AN - SCOPUS:84857025656
SN - 0195-6698
VL - 33
SP - 1086
EP - 1099
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
IS - 6
ER -