TY - JOUR

T1 - Fast embedding of spanning trees in biased Maker-Breaker games

AU - Hefetz, Dan

AU - Ferber, Asaf

AU - Krivelevich, Michael

PY - 2011/12/1

Y1 - 2011/12/1

N2 - Given a tree T=(V, E) on n vertices, we consider the (1:q) Maker-Breaker tree embedding game Tn. The board of this game is the edge set of the complete graph on n vertices. Maker wins Tn if and only if he 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 nε, Maker has a winning strategy for the (1:q) game Tn, for every q≤nα. 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 Tn. The board of this game is the edge set of the complete graph on n vertices. Maker wins Tn if and only if he 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 nε, Maker has a winning strategy for the (1:q) game Tn, for every q≤nα. Moreover, we prove that Maker can win this game within n+o(n) moves which is clearly asymptotically optimal.

KW - Embedding spanning trees

KW - Hamilton connected

KW - Maker-Breaker games

UR - http://www.scopus.com/inward/record.url?scp=82955216128&partnerID=8YFLogxK

U2 - 10.1016/j.endm.2011.09.054

DO - 10.1016/j.endm.2011.09.054

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AN - SCOPUS:82955216128

SN - 1571-0653

VL - 38

SP - 331

EP - 336

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

ER -